Preheat the oven to 350°F and grease a 12-cup muffin tin very well with cooking spray, or use a silicone muffin pan.
Melt the butter in a skillet over medium heat. Cook the onion and bell peppers for 5-6 minutes until soft, then add the ham and cook for 2 minutes more until lightly browned. Let cool for 5 minutes.
Blend the eggs, cottage cheese, salt, pepper and smoked paprika until completely smooth and frothy, about 30 seconds. This is the secret to a velvety, cafe-style texture that never turns rubbery.
Divide the ham and vegetable mixture and 1/2 cup of the cheddar evenly among the cups.
Pour the egg mixture over the fillings, filling each cup about 3/4 full. Top with the remaining cheddar and the chives.
Bake for 20-24 minutes, until the centers are just set and no longer jiggle. The muffins will puff up in the oven and settle slightly as they cool.
Cool for 5 minutes, then run a thin spatula around the edges to release them. Store in the refrigerator for up to 4 days and reheat for 30 seconds in the microwave.