In a large bowl, whisk together the eggs, milk, garlic, salt, and several grinds of pepper. Set aside.
Heat the olive oil in a 10 or 12-inch cast-iron skillet over medium heat. Add the scallions, broccoli, and a pinch of salt and pepper and cook, stirring occasionally, until the broccoli is tender but still bright green, 5 to 8 minutes. Stir in the smoked paprika, then add the egg mixture and gently shake the pan to distribute. Sprinkle with the feta and bake for 15 to 20 minutes, or until the eggs are set. Season to taste and serve.