For the caramelized onions:
2 large sweet or yellow onions, sliced into half-moons
2 tablespoons olive oil
1 tablespoon butter
Salt, to taste
Remaining sandwich ingredients:
3 English muffins, split and toasted
6 large eggs, whisked with a splash of water or milk
1 tablespoon butter
Salt and pepper, to taste
Make the caramelized onions: Heat a large, nonstick skillet to medium on the stove top. Add butter and oil and let the butter melt. Add onions and toss gently to coat all of the onion slices with the fat. Cook onions, stirring every 4-5 minutes, until the onions soften and turn a golden color -- the entire process should take about 25-30 minutes. Once onions are caramelized, season lightly with salt, remove from pan and set aside to cool.
To scramble the eggs, heat the remaining tablespoon of butter to medium-low in the same pan and season with salt and pepper. Add eggs and scrape the bottom of the pan with a rubber spatula every 1-2 minutes, until eggs are cooked through -- the entire process should take about 6-8 minutes.
To assemble the sandwiches, place one half of an English muffin, cut side up, on a work surface. Top with a scoop of scrambled eggs and a small scoop of caramelized onions. Serve immediately.