Preheat the oven to 400°F. Line 2 large baking sheets with parchment paper.
In the bowl of a stand mixer with the paddle attachment, combine flour, sugar, baking powder, salt, and nutmeg. Add butter and mix until it becomes a sand-like consistency.
In a separate bowl, combine milk, egg, and vanilla.
Slowly add the wet mixture to the flour mixture, mixing on low until a soft dough forms.
Fold the dough out onto a lightly floured surface, sprinkling flour on top of the dough.
Shape the dough into a circle, rolling it out to about ⅓-inch thick. Using a pizza cutter or a sharp knife, cut the dough into wedges, sprinkling more flour as needed (if the dough is too sticky).
Carefully place the wedges onto the lined baking sheets, leaving 1-2 inches between each wedge.
Bake 10-12 minutes, rotating the pans halfway through baking time, until golden brown.