Eggs do more different things in cooking than any other single ingredient, and nearly all of it comes down to protein coagulation at known temperatures.
The temperature ranges
White proteins begin setting at a lower temperature than yolk proteins.
Which is the basis of every technique producing a set white with a runny yolk.
Different proteins within each set at different points, which is why the transition is gradual rather than sudden and why texture changes continuously with temperature.
Overcooking squeezes water out of the protein network, producing rubbery whites and chalky yolks.
Scrambling
Low heat and constant movement produce small curds and a creamy result.
High heat produces large curds and expels water, which is the watery result on the plate.
Which means the choice between the two is a heat decision rather than a technique secret.
Removing from heat before they look done accounts for residual cooking, which continues in the pan.
Salt timing
Salting eggs in advance has been found to produce more tender scrambled eggs, since salt interferes with protein bonding.
Which is a small and testable effect, and fifteen minutes is generally cited as sufficient.
Boiling
Time and temperature determine the result, and starting temperature matters.
Eggs into already boiling water cook more predictably than eggs brought up from cold, since the timing starts from a known point.
Older eggs peel more easily, because the pH rises over time and the membrane adheres less.
Steaming rather than boiling has been found to improve peeling further, and cooling rapidly in cold water helps.
Poaching
Fresh eggs hold together better, since the white is thicker and less watery.
Which is the reverse of boiling, where older eggs are preferable.
Vinegar in the water encourages the white to set faster, and straining off the thin outer white before poaching does more.
Water should be barely trembling rather than boiling, since agitation tears the white apart.
Custards
Egg thickening a liquid, which requires holding below the point where the proteins bond too tightly and curdle.
Sugar raises the coagulation temperature, which widens the window and is why sweet custards are more forgiving than savoury ones.
Starch also stabilises, which is why pastry cream can be boiled and crème anglaise cannot.
Tempering — adding hot liquid gradually to the eggs before combining — raises their temperature slowly and prevents scrambling.
Foams
Whisking unfolds proteins which then form a network around air bubbles.
Fat interferes with this, which is why any yolk in the whites prevents them whipping and why bowls must be clean.
Acid stabilises the foam, which is why cream of tartar or lemon juice is added.
Sugar added gradually stabilises further, and added too early it inhibits volume.
Overwhipping breaks the network, producing a grainy separated mass that cannot be rescued.
Binding and enriching
Eggs bind mixtures by coagulating around other ingredients.
Yolks emulsify through lecithin, which is why they enrich sauces and doughs.
Which means a recipe specifying whole eggs, yolks or whites is specifying a function rather than a quantity, and substituting changes the result.
Sous vide and precise cooking
Holding eggs at a precise temperature produces textures unachievable by other methods.
Which is because the different proteins set at different points, so a temperature between them sets some and not others.
The results are genuinely distinctive and require equipment holding temperature accurately.
Freshness
Assessed by floating in water — a fresh egg sinks and lies flat, an older one stands or floats as the air cell grows.
Which is a reliable indicator of age and not of safety, and an egg that floats should be cracked separately and assessed by smell.
Storage
Practices differ between countries because of different processing.
Where eggs are washed, the protective cuticle is removed and refrigeration is required.
Where they are not washed, room temperature storage is normal.
Which is why advice differs internationally and why both are correct in their own context.
Substitutes
Different functions require different substitutes.
For binding, ground seeds with water or aquafaba work. For leavening, chemical raising agents. For emulsifying, lecithin or mustard.
Which means a single replacement rarely covers everything an egg was doing in a recipe.
Size and recipes
Egg sizes are graded by weight ranges, and a recipe assumes one.
Which matters most in baking, where the liquid and protein contribution is structural.
Weighing eggs out of shell is the reliable approach for anything where precision matters.
Colour
Shell colour reflects the breed of hen and has no bearing on nutrition or flavour.
Yolk colour reflects the hen's diet, and it is frequently manipulated through feed additives, so a deep colour indicates feed rather than quality.
Cracking and separating
Cracking on a flat surface rather than an edge produces fewer shell fragments, since the edge pushes shell inward.
Separating is easiest when the eggs are cold, since the yolk membrane is firmer and less likely to break.
Whites whip better at room temperature, which is why the usual advice is to separate cold and then let the whites warm.