Prepare Oven and Pan: Preheat your oven to 340°F (170°C, or 150°C for fan-assisted ovens, Gas Mark 3). Thoroughly grease 9 cups of a standard 12-hole muffin pan with your choice of butter or olive oil/spray.
Combine Wet Ingredients: In a spacious mixing bowl, crack the eggs. Whisk them vigorously until they are uniformly smooth and slightly frothy.
Incorporate Cheeses & Aromatics: To the whisked eggs, add the full-fat cottage cheese, shredded cheddar cheese, finely chopped scallions, finely chopped sun-dried tomatoes, dried oregano, fine sea salt, and a few grinds of black pepper. Stir these ingredients together with the whisk until everything is thoroughly combined and evenly distributed throughout the mixture.
Add Dry Ingredients: Place a sifter over the bowl (if using) and add the all-purpose flour and baking powder. Sift them into the wet mixture. Using a spatula or gently with the whisk, fold these dry ingredients into the wet batter. Continue mixing only until the flour streaks are no longer visible. Be careful not to overmix, as this will help maintain a tender and fluffy final texture (see Note 2).
Fill Muffin Cups: Carefully and evenly spoon the prepared egg batter into the 9 greased muffin cups. Aim to fill them about equally, usually two-thirds to three-quarters full.
Bake: Transfer the muffin pan to the center rack of your preheated oven. Bake for 35-40 minutes. The Savory Sunrise Egg Clouds are done when they are puffed up, exhibit a light golden-brown top, and a wooden skewer or toothpick inserted into the center of a muffin comes out clean.
Cool Before Serving: Once baked, carefully remove the muffin pan from the oven. Allow the egg clouds to cool directly in the pan for a minimum of 10-15 minutes. This resting period is important as it helps them to set properly and makes them easier to remove without damage (see Note 3).
Serve: Gently remove the muffins from the pan. These egg clouds are most delightful when served warm.