Heat oven to 350° F. In a medium bowl, whisk together the flour, baking soda, cinnamon, salt, and nutmeg.
Using an electric mixer, beat the butter and sugars on medium-high speed until fluffy, 2 to 3 minutes. One at a time, beat in the eggs, then the vanilla. Reduce speed to low and gradually add the flour mixture, mixing until just combined (do not overmix). Mix in the oats and raisins by hand.
Drop heaping tablespoonfuls of the dough onto baking sheets, spacing them 2 inches apart.
Bake, rotating the baking sheets halfway through, until golden, 12 to 14 minutes. Cool slightly on the baking sheets, then transfer to wire racks to cool completely. Store the cookies in an airtight container at room temperature for up to 5 days.
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