Preheat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, baking powder, baking soda, salt, and spices in a bowl.
Cream butter with brown sugar and granulated sugar until fluffy.
Beat in egg and vanilla, then mix in milk.
Add dry ingredients. Mix on low just until combined.
Fold in carrots and pecans. Chill 10 minutes if dough is soft.
Scoop 1.5-tablespoon mounds onto sheets, spacing 2 inches.
Bake 11–13 minutes, until edges set and tops look dry.
Cool 5 minutes on sheet, then move to a rack.