European custards depend on eggs to thicken milk, while Indian milk puddings use none. The thickening comes from reduction and from starch, and the two approaches produce quite different desserts.
Egg thickening works by protein coagulation
Egg proteins unfold and bond into a loose mesh as they heat, trapping liquid and setting the mixture. The process happens within a narrow temperature range.
Above that range the proteins bond too tightly and squeeze liquid out, which is the curdling that custard technique is designed to prevent.
The entire discipline of gentle heat, constant stirring and water baths exists to keep an egg mixture inside that window.
Reduction thickens by removing water instead
Kheer is simmered for a long time with the milk gradually losing water. Its own solids, fat, protein and sugar concentrate, and the liquid thickens as a direct result.
Because there is no protein set to overshoot, the mixture cannot curdle from overheating in the way a custard can. It can scorch on the base, which is why stirring is still required.
Grain starch does the rest of the work
Rice, vermicelli or tapioca cooked in the milk release starch that gelatinizes and thickens the surrounding liquid, adding body beyond what reduction alone provides.
That starch also holds water, so the pudding thickens further as it cools and the starch network sets. Kheer served warm and the same kheer cold are noticeably different in consistency.
Different grains give different results, with broken short rice releasing starch readily and vermicelli releasing much less, which is why the two versions have distinct textures.
The absence of eggs is partly dietary
A large vegetarian population that excludes eggs but includes dairy shaped what the sweet repertoire could be built from, and dairy reduction became the dominant technique.
That constraint is also why milk solids, rather than butter and eggs, are the structural basis of so much Indian confectionery.
It also kept the technique portable, since a pot of milk and a handful of grain were available in kitchens that had no oven and no reliable supply of eggs.
What this means for the cook
The method is slow but forgiving, needing time and attention to the base of the pan rather than temperature precision or a thermometer.
Whole milk gives the reduction something to concentrate, and reduced-fat milk produces a thin result no amount of extra simmering fully corrects. That is the single most consequential ingredient choice in an American kitchen.