Set the oven to 350°F. Generously spray a 12-cup muffin tin with nonstick spray or lightly oil each cup so the egg bites release easily.
In a medium bowl, whisk the eggs with sea salt and smoked paprika until the yolks and whites are well combined and slightly frothy.
Transfer the whisked eggs to a blender, add the cottage cheese, and pulse 6–8 times until the mixture is smooth and creamy. The blender gives the bites a silky texture.
Fold the chopped sun-dried tomatoes, chopped spinach and torn basil into the egg-cottage cheese mixture by hand so the pieces stay intact and distribute evenly.
Divide the mixture among the 12 muffin cups (about 1/4 cup per cup). Smooth the tops slightly and sprinkle each cup with a little crumbled feta and a pinch of grated Parmesan. Finish with a light twist of black pepper.
Bake in the middle of the oven for 18–22 minutes, until the centers are set and the edges are lightly golden. If you want a touch of color on top, place under the broiler for 1 minute — watch closely so they don't burn.
Remove the pan and let the egg bites rest in the tin for 8–10 minutes; this helps them finish cooking gently and makes them easier to remove. Transfer to a wire rack before serving.
Serve warm or room temperature. Refrigerate leftovers in an airtight container for up to 5 days and reheat gently in the microwave or oven.