Whisk egg yolks, water, salt, chile powder and paprika together until completely blended.
Juice a few limes until you have three to four tablespoons. Ensure it's free of any seeds or pulp, and set aside.
Cut two full sticks of cold, unsalted butter (to be clear, that's two 4oz sticks) into 1/4" thick slices, on a plate. The warming of the butter in the pan will serve as a temperature regulator to the overall sauce as it's coming together.
Add mixture to a warm (you should still barely be able to touch the center) cast iron skillet. Turn heat up to medium-low (on a 1-8 scale burner I mean no more than a 3). The key thing here is you do NOT want to rapidly raise the heat. Doing so will result in the egg yolk forming curds faster than you can blend them.
Do. Not. Stop. Whisking. Keep your whisk moving and constantly breaking up any curds you may start to see form. Imaging moving the whisk as if it were a paint brush, and you were trying to paint the whole surface of the skillet.
Add 3-4 of your butter slices at a time, and whisk as they melt into the sauce. Repeat. Once half of your butter is added to the skillet, add half of your lime juice, keep whisking, and continue with your butter. Once the last of the butter is added, add the last of the lime juice and the sugar. Thoroughly whisk. Did I mention to whisk?
Remove from heat and set pan on a trivet or cold burner, where it will remain warm until dish is assembled.