Indian sweets that set in a slab are poured into shallow metal trays of a fairly consistent depth. The dimensions are not tradition for its own sake; they control how the sweet cools and sets.
Depth determines the cooling rate
A hot sugar and dairy mixture sets as it cools, and the rate of cooling determines the size of the crystals that form.
Poured thin, the mixture loses heat quickly and crystallizes into fine grains, which is what gives a smooth barfi its close, even texture.
Poured deep, the center stays hot far longer, crystals grow larger, and the finished sweet is coarser in the middle than at the edges.
Metal is doing work that ceramic cannot
Steel and aluminum trays conduct heat away rapidly, pulling it from the underside of the slab as fast as the surface loses it to the air.
A glass or ceramic dish insulates instead, so the mixture cools mainly from the top and sets unevenly through its thickness.
This is why a recipe that behaves reliably in a sweet shop can fail in a home kitchen using a baking dish, with no change in the cooking itself.
Thickness is decided before the mixture is poured
The intended piece is usually a specific thickness, thin enough to eat in a bite or two and thick enough to hold together when lifted.
A cook controls that by matching tray area to batch volume rather than by spreading the mixture out afterwards, since a setting mixture cannot be redistributed.
Trays that are too large give a thin, fragile sheet; too small and the slab is deep enough to be heavy and to set unevenly.
Greasing and lining decide whether it releases
The tray is greased before pouring, usually with ghee, so the slab lifts cleanly once set. Sugar-rich mixtures bond firmly to bare metal.
Some sweets are set on edible sheets or a dusting of flour or nut powder, which serves the same purpose and stays on the finished piece.
Parchment works in a home kitchen but slightly slows the heat transfer, so a slab set on paper takes longer and can end up softer.
Cutting timing depends on the same variables
Sweets are scored while still warm and separated once fully cold, because a fully set slab cracks rather than cutting and a warm one smears.
A shallow slab reaches that window sooner and passes through it faster, so a cook working with a thin tray has less time to score than the recipe assumes.
An ordinary quarter sheet pan is a reasonable American substitute, since it is metal, shallow and close to the proportions the recipes were written around.