Preheat the oven to 375°F and grease or line a 12-cup muffin tin.
Place the broccoli in a microwave-safe bowl with the water, cover and microwave for 2 minutes until bright green and barely tender. Drain and spread on a towel to cool and dry, so the muffins bake up fluffy instead of soggy.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, garlic powder, onion powder, mustard powder and pepper.
In a separate bowl, whisk the cottage cheese, eggs, milk and melted butter. Leave the curds whole, since they melt into creamy, cheesy pockets as the muffins bake.
Add the wet mixture to the dry ingredients and stir halfway. Add the broccoli, 1 1/4 cups cheddar and green onions, then fold just until no dry flour remains.
Divide the batter among the cups and top with the remaining 1/4 cup cheddar.
Bake for 22-25 minutes, until golden brown, the cheese is bubbly and a toothpick comes out free of raw batter.
Cool in the pan for 5 minutes, then loosen the edges with a thin spatula. Serve warm, or reheat leftovers for 15 seconds in the microwave.