Arrange a rack in the middle of the oven and heat to 400°F. Generously coat a 12-well standard muffin tin with cooking spray or olive oil.
Evenly divide the shallot, broccoli, cottage cheese, and cheddar between the muffin wells.
Place the eggs, milk, salt, and pepper in a large bowl and whisk until the eggs are completely incorporated. Pour into the muffin wells, filling each 1/2 to 3/4 full.
Bake until the muffins are set and lightly browned around the edges, 12 to 14 minutes. Place the pan on a wire rack and let cool for 2 to 3 minutes. Run a butter knife around each cup to the loosen the muffins before removing them from the pan.