Heat the oven to 350 degrees F and arrange a rack in the middle. Place flour, baking powder salt, cinnamon, and nutmeg in a medium bowl and whisk to combine; set aside.
Combine butter and sugar in a large bowl and beat over medium speed until mixture resembles wet sand and is airy, about 3 minutes. Add eggs 1 at a time, letting each fully incorporate before adding the next. Add vanilla extract. Reduce speed to low, add flour mixture in 2 parts, and mix until just combined, about 1 minute. Add remaining ingredients and mix until evenly combined.
Using a 2-inch ice cream scoop, drop dough onto baking sheets, spaced about 1-inch apart. Bake until cookies are puffed, set, and tops and undersides are golden brown, rotating sheets halfway through, about 18 to 20 minutes. Remove from oven, let cool on sheets 2 minutes, then remove to wire racks to cool completely.