Adjust oven racks to the upper-middle and lower-middle positions. Preheat oven to 350 degrees. Line 2 rimmed baking sheets with parchment paper or silicone mats.
In a medium bowl or on a piece of parchment paper, sift together flour, baking soda, cinnamon, nutmeg, and salt. Set aside.
In a standing mixer fit with the paddle attachment, or with an electric mixer on high speed, cream butter until pale and fluffy. Add the granulated and brown sugars and beat until the mixture is smooth.
Add egg and vanilla and beat on low speed until blended, scraping down the sides of the bowl as necessary.
Add the flour mixture in batches (about 1/4 cup at a time) and mix on low speed until just blended. Add the oats and raisins and stir until just combined.
Working with 1 heaping tablespoon of dough at a time, scoop dough into 1 1/2-inch balls and drop on prepared baking sheets about 2 inches apart. (I use the OXO medium cookie scoop, a size 40 portioner, and do 12 scoops of dough per baking sheet). You should have 24 cookies.
Bake until the cookies are golden brown, about 12-15 minutes. Transfer to wire racks and cool completely.