Preheat your oven to 340°F (170°C; 150°C for fan-assisted ovens). 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: In a small bowl, whisk together the all-purpose flour and baking powder. Sift this mixture over the wet ingredients. Using a spatula, fold just until no flour streaks remain (do not overmix). 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. Bake for 35–40 minutes, until puffed and light golden and a skewer comes out clean -or the center of a muffin registers 165°F (74°C)-.
Cool Before Serving: Remove the pan from the oven and cool in the pan for 10–15 minutes to set. Run a thin knife around each muffin before unmolding (see Note 3).
Serve: Gently remove the muffins from the pan. These egg clouds are most delightful when served warm.