Carrot halwa is grated carrot cooked down in milk until almost nothing liquid remains. Because the carrot is most of the dish, which carrots are used changes the result substantially.
The method is concentration, not flavoring
Both the carrot and the milk lose water over a long slow cook, and their solids concentrate into a single mass. There is no thickener and no flour involved.
Milk sugars and proteins brown gently during that reduction, contributing a cooked-dairy depth that is a large part of the finished flavor.
The carrot's own sugar concentrates in parallel, which is why a sweeter carrot needs less added sugar and produces a rounder result.
Water content sets the cooking time
A watery carrot releases more liquid, so the pan takes considerably longer to reduce and the carrot spends more time cooking before the mixture tightens.
Extended cooking softens the shreds past the point where they hold any bite, and the halwa becomes a paste rather than a mass of distinguishable strands.
Indian winter carrots are a different vegetable
The red carrots sold in northern India in winter are notably sweeter, deeper in color and lower in water than the orange storage carrots common in American supermarkets.
Those properties are why the dish is traditionally seasonal, and why halwa made at other times of year in India is considered a lesser version of the same dessert.
The color difference is also visible in the finished dish, which is deep red rather than the orange an American carrot produces.
Grating size matters more than it appears
Fine shreds release their water quickly and break down early, giving a smooth halwa with little texture. Coarse shreds hold their form and give a more distinctly stranded result.
Most recipes assume a medium grate, and using a food processor's fine disc is a common cause of a halwa that turns to paste well before the milk has reduced.
Sourcing in the United States
Indian grocery stores sometimes carry red carrots seasonally, and farmers markets stock varieties closer to the traditional profile than the bagged supermarket standard.
With ordinary orange carrots, the workable adjustments are to grate coarsely, cook the carrots down before the milk goes in to drive off water early, and taste before deciding how much sugar the batch actually needs.