Preheat your oven to 200°C (400°F) and line a baking tray with parchment paper. In a large bowl, whisk together the all-purpose flour, baking powder, and salt. Add the cold, cubed butter and incorporate it using your fingertips or a pastry cutter until the mixture resembles coarse crumbs.
Fold in the grated cheese, distributing it evenly. Gradually pour in the milk, stirring gently until a soft dough comes together. Be careful not to overmix, as this will ensure the buns remain light and tender.
Lightly dust your work surface with flour and roll out the dough to approximately 1/2 inch in thickness. Using a heart-shaped cookie cutter, cut out the buns. Gather and re-roll the dough scraps to cut additional hearts until all the dough is used.
Arrange the heart-shaped buns on the prepared baking sheet, spacing them slightly apart. Beat the egg to create an egg wash and brush it lightly over each bun. Sprinkle additional grated cheese on top for a golden, cheesy crust.
Bake in the preheated oven for 12–15 minutes, or until the buns are puffed and golden, with the cheese topping bubbling.
Once baked, remove the buns from the oven and transfer them to a wire rack to cool slightly. Serve warm as a savory snack or pair with your favorite soup or salad for a delightful addition to any meal.