Heat olive oil in an ovenproof skillet over medium heat; cook onion and garlic until soft and translucent, about 5 minutes. Add soy chorizo and cook, stirring often, until hot, about 5 minutes.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Beat eggs, milk, and salt in a small bowl. Pour into skillet and stir gently to make sure egg mixture reaches the bottom of skillet. Cook until eggs are set on the bottom and almost set on the top, about 5 minutes.
Transfer skillet to the preheated oven and broil until the top is set and starts to brown, 3 to 5 minutes. Let rest 5 minutes before serving.
