Chop butter into 1/4-inch pieces and return it to the refrigerator to keep it cold until needed.
Preheat oven to 400°F and line a baking sheet with parchment paper or grease it with butter.
Add flour, baking powder, salt, rosemary, and lemon zest to a large bowl; whisk to combine.
Add chopped butter and cheese to dry ingredients, mixing once or twice to coat ingredients with flour.
Working quickly with your fingers or a pastry blender, rub or cut the butter and cheese into the flour until it resembles coarse meal.
Drizzle most of the milk over the mixture and toss until a sticky, thick dough forms, adding more milk if the mixture includes dry bits that don't incorporate easily. Take care not to over-mix.
Using a 1/4-cup cookie scoop, transfer mounds of dough to the prepared baking sheet.
Bake the biscuits until golden brown, about 20 to 25 minutes.
Let the biscuits cool slightly on baking sheets before transferring to a wire rack. Serve warm or at room temperature.