Preheat the oven to 400F and line a large baking sheet with parchment paper.
Shred the zucchini and press it dry between paper towels. A firm squeeze is enough.
Cook the sausage in a skillet over medium heat, breaking it into crumbles, until mostly browned. Add the pressed zucchini and cook together until the pan looks dry and no liquid pools, turning the heat up a touch near the end to drive off moisture. Drain excess grease and let cool.
In a large bowl, whisk the eggs with the cottage cheese and all the seasonings until fairly smooth.
Fold in the flour and baking powder until no streaks remain, being careful not to overmix. Fold in the cooled sausage and zucchini mixture and 1/4 cup of the shredded cheese.
Check the consistency. The batter should mound on a spoon and hold a soft peak. If it spreads or slumps, add flour 2 tablespoons at a time until it holds. If it is stiff and dry, add a splash of milk.
Drop 1/4-cup mounds onto the sheet, leaving 2 inches between them, and sprinkle with the remaining 1/4 cup cheese. Bake 18 to 22 minutes, until golden and set. Cool 5 minutes before moving.