Heat the olive oil in a large pan set over medium heat. Add the onion and hot pepper and cook, stirring occasionally, until softened, 6 to 8 minutes. Add the garlic, nutmeg, and salt, and cook, stirring, until fragrant, 1 to 2 minutes​.

Add the spinach and lemon juice to the pan, turn the heat to low, cover, and cook, tossing occasionally with tongs, until the spinach is very soft, 7 to 10 minutes. (If the spinach does not fit all at once in the pan, add a little at a time, adding more as it wilts and loses volume.)

Uncover. Using the back of a spoon, press the mixture down a little so that it has the same depth everywhere and make four shallow indentations​ on the surface of the greens mixture to hold the eggs while they cook.

Break the eggs one at a time into a small cup and gently slide them into the indentations. Raise the heat to medium, cover the pan, and cook until the whites are set but the yolks are still a bit runny, 4 to 5 minutes, or to desired doneness. Remove the pan​ from the heat. Drizzle a little more olive oil on top and sprinkle with pepper, dill and feta. Serve hot, directly from the pan.