Heat the oven to 350 F / 175 C. Rub 1 tsp of the butter over the bottom and sides of a 9-inch / 23 cm deep pie dish.
Melt the remaining butter in a 10-inch / 25 cm skillet over medium heat. Add the onion and cook for 4 to 5 minutes until soft.
Add the garlic and broccoli to the skillet. Cook for 3 minutes, stirring, until the broccoli turns bright green and just tender. Remove from heat and let cool for 5 minutes.
In a large mixing bowl, whisk the eggs for about a minute until the yolks and whites are fully combined.
Add the cottage cheese and milk to the eggs. Whisk for another minute until mostly smooth, small curds are fine.
Stir in 1 1/2 cups of the cheddar, the cooled broccoli mixture, salt, and pepper until evenly combined.
Pour the mixture into the prepared dish. Scatter the remaining 1/2 cup cheddar over the top.
Bake for 40 to 45 minutes, until the center is set and no longer jiggly and the edges are puffed and light golden. Check with an instant-read thermometer, the center should read 165 F / 74 C.
Cool on a rack for 10 minutes before slicing into wedges. This lets the custard finish setting so the slices hold their shape.