Preheat oven to 425°F and line a baking sheet with parchment paper. In a large bowl, mix flour, baking powder, salt, and baking soda if using. Cut cold butter into flour using a pastry cutter or fork until mixture resembles coarse crumbs with pea-sized butter bits.
2 cups all-purpose flour, 1 tbsp baking powder, 1 tsp salt, 0.5 cup unsalted butter, 0.25 tsp baking soda
Gently fold shredded cheddar cheese and optional chopped herbs into the flour mixture. Add milk and stir with a fork just until dough comes together, leaving flour streaks visible for a shaggy, slightly sticky texture.
1 cup sharp cheddar cheese, 0.75 cup whole milk or buttermilk, fresh chives or thyme
Drop ¼-cup portions of dough onto the prepared baking sheet, spacing them about 1 inch apart. Do not smooth the tops to keep rustic, uneven shapes for crisp edges.
2 cups all-purpose flour, 1 cup sharp cheddar cheese
Bake in the preheated oven for 12-15 minutes, until tops are golden brown and edges look set. Confirm doneness by inserting a toothpick in the center; it should come out clean. Let biscuits cool on the pan for 5 minutes before serving.
While biscuits bake, heat butter in a non-stick skillet over medium heat. Crack eggs directly into the pan for fried eggs or whisk and scramble over medium-low heat until just set. Season eggs with salt and black pepper to taste.
6 large eggs, black pepper, butter