Preheat the oven to 425°F and line a large baking sheet with parchment paper.
Blend the cottage cheese and egg until completely smooth and creamy. This smooth base replaces most of the butter and milk, keeping the biscuits moist while packing in protein.
Whisk the flour, baking powder, salt, garlic powder and black pepper in a large bowl. Cut in the cold butter with a pastry blender or your fingertips until the pieces are about the size of peas.
Add the cheddar, ham and chives to the flour mixture and toss until evenly distributed and coated in flour.
Pour in the blended cottage cheese mixture and fold with a spatula just until no dry flour remains. The dough will be thick and sticky, which is exactly what you want for soft, tender drop biscuits.
Scoop 1/3 cup mounds of dough onto the baking sheet about 2 inches apart, making 10 biscuits. Bake for 16-19 minutes, until golden brown on top and set in the center.
Let the biscuits cool for 5 minutes before serving. Store leftovers in the refrigerator for up to 4 days and rewarm in the oven or microwave for a quick grab-and-go breakfast.