Whisk eggs, milk, salt, and pepper in a bowl.
Heat butter in a skillet over medium-low heat. Add eggs and scramble until barely set, about 1-2 minutes.
Add beans, chilis, salsa, and pepper jack. Gently stir to combine. Reduce heat to low, cover, and cook until cheese melts, about 2-3 minutes.
To serve, top with green onion.
