Preheat oven to 350°F. Lightly spray a nonstick 12-cup muffin pan with extra-virgin olive oil spray, coating the bottoms and sides well.
Heat the olive oil in a large skillet over medium heat. Add the broccoli, red bell pepper, and onion and cook for 5–7 minutes, stirring occasionally, until the vegetables begin to soften and some of their moisture has cooked off.
Add the spinach to the skillet and cook for another 1–2 minutes, until wilted. Remove from the heat and let cool for about 5 minutes.
In a large bowl, whisk the eggs until combined. Add the cottage cheese, ground flaxseed, salt, garlic powder, black pepper, and red pepper flakes, if using. Whisk until evenly incorporated. Small cottage cheese curds will remain.
Stir in the cheddar and slightly cooled vegetables until evenly distributed.
Using a ⅓-cup measuring cup, divide the mixture among the muffin cups, starting with a scant ⅓ cup in each. Distribute any remaining mixture among cups that have room, being careful not to fill them to the top.
Bake for 18–20 minutes, checking at 18 minutes, until the centers are set. Avoid overbaking; the muffins do not need to be deeply browned.
Let the muffins cool in the pan for about 5 minutes. Run a small silicone spatula or plastic knife gently around the edges of each muffin to loosen, then carefully lift them out.