Heat 1 teaspoon of the butter in an 8-inch nonstick skillet over medium heat. Cook the pepper and onion for 3 minutes until soft, add the spinach and stir until wilted. Transfer the filling to a plate and wipe the pan.
Beat the eggs with the milk and salt until the whites and yolks are completely combined.
Return the pan to medium heat with the remaining butter. When it foams, pour in the eggs.
Let the eggs set for a few seconds, then push the edges toward the center with a spatula, tilting the pan so the uncooked egg flows underneath. Repeat until the top is softly set but still slightly glossy, about 1–2 minutes.
Scatter the filling and cheese over one half. Fold the other half over, cook for 30 seconds more so the cheese melts, and slide onto a plate. Finish with pepper and chives.