Thandai is built from almonds, melon seeds, peppercorns and fennel worked into a paste before milk is added. Grinding rather than steeping is what makes the drink what it is.
Nuts hold their flavor inside cell walls
An almond dropped whole into warm milk gives up very little. Its oils, proteins and aromatic compounds sit inside intact cells that milk cannot penetrate in any reasonable time.
Grinding ruptures those cells mechanically. The oil and protein are released into the surrounding liquid, where they can disperse rather than stay locked in the solid.
This is why the traditional method soaks the nuts first. Hydrated tissue tears rather than shatters, giving a smoother paste and releasing more of the interior than dry grinding does.
The paste is the thickener
Ground nut solids do more than flavor the milk. Suspended particles and released oil raise the viscosity, giving thandai its characteristic body without any starch, cream or gum.
The nut oil is not free-floating either. Nut proteins released by the same grinding act as emulsifiers, holding the oil in suspension so the drink does not separate immediately.
A drink made by steeping whole spices in milk and straining them out has flavor but no body. It is a spiced milk rather than thandai.
Seeds and spices behave differently from each other
Fennel, peppercorn and cardamom carry volatile aromatics that survive grinding but escape quickly once released. That is why the paste is used soon after it is made rather than stored for weeks.
Melon and poppy seeds contribute almost no aroma. Their role is textural, adding fine solids that make the mouthfeel dense without adding the fat load of more almonds.
Straining is a texture decision
Passing the milk through a cloth removes coarse particles and leaves a smoother drink, at the cost of some of the solids that provide body. Household practice varies on how fine to strain.
Skipping the strain entirely gives a grainy drink that settles fast. Most versions land in between, straining out the husk and gritty fragments while keeping the fine paste in suspension.
Making it in an American kitchen
A high-speed blender does the job of a stone grinder but heats the paste through friction, which drives off aromatics. Working in short pulses with cold soaked nuts limits that.
US supermarkets carry almonds and fennel easily; melon seeds, poppy seeds and green cardamom are Indian grocery items. The premixed thandai pastes sold there are a reasonable shortcut when the whole ingredient list is unavailable.