Heat oven to 350 F / 175 C. Grease a 12-cup muffin tin generously with butter, right on the metal, not paper liners, since egg sticks to paper no matter how well you spray it.
Heat olive oil in an 8-inch nonstick skillet over medium heat. Add spinach and cook 2 to 3 minutes, stirring, until wilted. Transfer to a clean towel and squeeze out as much liquid as you can.
In a large mixing bowl, whisk the eggs, egg whites, cottage cheese, salt, pepper and garlic powder until mostly smooth (small curds of cottage cheese are fine).
Divide the diced ham, wilted spinach and feta evenly among the 12 muffin cups.
Ladle the egg mixture over the filling in each cup, filling to about 3/4 full to leave room for puffing.
Bake for 18 to 22 minutes, until the centers are set, no longer jiggly, and a thermometer inserted into the middle reads 160 F / 71 C.
Cool the cups in the tin for 5 minutes, then run a thin knife around the edge of each one and lift out onto a wire rack.
Serve warm, or cool completely before storing.