Cook the onion in 1 tbsp butter with a pinch of salt over medium-low heat, stirring now and then, 25 minutes until deep brown and jammy.
Mix the mayo and sriracha. Split and lightly toast the buns.
Beat the eggs with a pinch of salt. Melt the rest of the butter over very low heat, add the eggs and stir constantly until they form small, glossy curds, 3 to 4 minutes. Take off the heat while still a little wet.
Lay cheese on the bottom bun, pile on the eggs, then the onions and chives, sriracha mayo on the top bun, and close.
Tips
Pull the eggs early: they keep cooking on the bun.