In a medium bowl, whisk together the all-purpose flour, baking soda, cinnamon, salt, and nutmeg until well combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, brown sugar, and granulated sugar on medium speed until light and creamy. Add the eggs and vanilla extract, and continue mixing until everything is fully incorporated, scraping down the sides of the bowl as needed.
With the mixer on low speed, slowly add the dry flour mixture and mix until just combined. Then mix in the oats and raisins on low speed, being careful not to overmix.
Cover the bowl with plastic wrap and refrigerate the dough for 1 to 2 hours. Chilling the dough helps the cookies hold their shape, but avoid refrigerating for too long, as it can cause the edges to brown too quickly while the centers remain underdone.
When ready to bake, preheat the oven to 350°F and line baking sheets with parchment paper.
Scoop rounded tablespoons of dough, shape into balls, and place them on the prepared baking sheets, leaving space between each for spreading.
Bake for 9–11 minutes, until the edges are just turning golden and the centers are still slightly soft. Be careful not to overbake — for soft and chewy cookies, it's best to slightly underbake them. If baking two trays at once, rotate them halfway through for even baking.
Let the cookies cool on the baking sheet for 5–10 minutes before transferring them to a wire rack to cool completely.