Preheat the oven to 350°F and adjust the rack to the middle position. In a bowl, whisk together the eggs, milk, and ¼ teaspoon salt until well combined.

Heat oil in an 8-inch oven-safe nonstick skillet over medium-high heat. Once shimmering, add the broccoli, red pepper flakes, and remaining ⅛ teaspoon salt. Cook, stirring frequently, until the broccoli is crisp-tender and slightly browned, about 4 to 6 minutes.

Add 1½ tablespoons of water, lemon zest, and lemon juice to the skillet. Stir constantly until the broccoli is just tender and the liquid evaporates, about 30 seconds.

Pour in the feta and egg mixture. Stir gently with a rubber spatula until large curds form, leaving some liquid eggs, about 30 seconds. Smooth the mixture into an even layer and let cook undisturbed for another 30 seconds.

Transfer the skillet to the oven and bake until the frittata is slightly puffy and the surface bounces back when pressed, about 6 to 9 minutes.

Carefully loosen the frittata with a rubber spatula and transfer it to a cutting board. Let it sit for 5 minutes before slicing and serving.