Preheat your oven to 325°F and position racks so one is at the bottom and one in the middle. While the oven heats, grease a standard 12-cup muffin pan with cooking spray or butter, ensuring each cup is well coated to prevent sticking. Fill a baking dish with water and set it aside—this water bath will create steam in the oven, which keeps the egg bites tender and prevents them from drying out. Measure out all ingredients and have them ready before you begin blending.
Add the room-temperature eggs, cottage cheese, salt, and pepper to a blender. Blend on medium speed for about 30 seconds until the mixture is smooth and well combined—the cottage cheese should be fully incorporated with no lumps. Room-temperature eggs blend more smoothly and incorporate air better than cold ones, which creates a lighter texture in the final bites.
Pour the egg mixture from Step 2 into a large bowl. Add the crumbled feta, spinach, oregano, and garlic powder, then gently fold everything together with a rubber spatula until the ingredients are evenly distributed—don't overmix, as you want to keep the texture light. I like to crumble the feta into small pea-sized pieces so it distributes evenly throughout the bites and gives you a bit in every bite.
Carefully pour the egg mixture into the prepared muffin cups, filling each about halfway full—this leaves room for the bites to rise slightly as they cook. Place the greased muffin pan on the middle oven rack. Slide the dish with hot water onto the bottom rack, positioning it so steam can rise around the muffin pan above it.
Bake for 18 to 22 minutes, until the egg bites are set but still slightly jiggly in the very center when gently shaken—they will continue to cook slightly as they cool. The tops should look just set and be lightly golden. Remove from the oven and let the bites rest in the pan for 2-3 minutes before serving, as this helps them firm up slightly and makes them easier to remove. I prefer to let them cool just slightly before eating so the flavors come through more clearly, though they're delicious warm right out of the oven too.