Combine Brown Sugar, Coconut Milk, and Salt in a medium saucepan. Place over medium heat, and stir occasionally to form a homogenous mixture. We want to heat this up to just before it starts boiling - small bubbles gently popping at the surface with some visible steam.
As mixture on the stove is heating up, separate your 4 egg yolks and mix gently in a heat-proof bowl to break them up.
You may want to put on some music as the next steps will have you busy stirring for 10-15 minutes straight - your patience will be rewarded.
Once mixture is simmering with gentle bubbles, but not quite boiling, pour half (just estimate) into your yolks while whisking rapidly. Once thoroughly mixed, about 5 to 10 seconds, pour the yolk mixture back into the pot. Turn heat down to medium-low and cook while whisking constantly for 10-15 minutes. You'll see some gentle bubbles popping at surface and that's good. We cook for so long here for two reasons: to thicken the curd into a luxurious spread and to evaporate water out to intensify the flavor. If you like a thick spread, cook closer to 15 minutes. If you're unsure, remember the curd will thicken up a bit more once it's cooled down - you can't really go wrong, don't overthink it.
Once curd is finished, remove from heat. You can put it through a fine sieve here for a super creamy, smooth final product, but if you stir constantly this won't be necessary.