Pre-heat the oven to 375°F
Move oven racks to the top and bottom slots.
Line 2 baking sheets with silicone baking mats or parchment paper.
Combine milk, butter, salt, and pepper in a medium saucepan and bring to a boil over medium heat. Reduce heat to low, add ﬂour all at once, and stir quickly until all the flour is wet and forms a ball.
Cook, stirring constantly, until dough feels dry to the touch and is no longer sticking to the bottom of the pan, about 3 to 5 minutes. It is important to dry the dough completely because we are going to add the eggs next.
Transfer dough to a mixer ﬁtted with a paddle attachment; mix dough to cool it down to less than 140 °F. so you don’t “cook” the eggs.
Beat in eggs one at a time on medium-low speed, letting the ﬁrst one completely incorporate before adding the next.
Reserve 3 tablespoons of the shredded Manchego cheese. Add remaining Manchego and Parmesan cheese to dough and mix on low until incorporated. Drop tablespoon-size rounds of dough on the prepared baking sheets, about 1/2 inch apart.
You can also use a piping bag with a plain tip, and pipe small balls onto the baking sheets.
Evenly sprinkle reserved Manchego cheese over top.
Bake, rotating halfway through baking time, until puffed and golden brown, about 30 to 35 minutes. Serve hot, warm, or at room temperature.