In a skillet, melt 1 tablespoon of unsalted butter with the cooking oil over medium heat.

Add the sliced onion and sauté until caramelized, about 10 minutes.

Add the water to the skillet, cover, and let steam for 2 minutes.

In a bowl, whisk the eggs, then stir in the chives, salt, and pepper.

Push the onions to the side of the skillet and pour the egg mixture into the empty side, scrambling the eggs until cooked.

Once the eggs are cooked, mix with the onions and remove from heat.

Spread the mayonnaise and Sriracha on the brioche bun.

Layer the egg and onion mixture onto the bun, topping with cheddar cheese.