Adjust oven rack to middle position and preheat oven to 350°F. Line 2 baking sheets with parchment paper.
In a large bowl, mix together sugars, eggs, and butter. Stir in peanut butter, vanilla, nutmeg, and cinnamon. Add flour and baking soda and mix until dough forms.
Drop mounds of dough by the tablespoonful onto prepared baking sheets, spacing about 2" apart. Lightly press tops of cookies with tines of a fork.
Bake cookies rotating trays halfway through, until golden brown, 10–12 minutes. Transfer to a wire rack and let cool slightly.