Weigh or measure both sugars into a bowl and set aside. In a separate bowl, weigh or measure the flour, then add the baking soda, baking powder, salt, cinnamon, nutmeg, and allspice. Whisk to blend the dry ingredients. If your raisins seem dry, soak them in warm water for 10–15 minutes to plump them and add moisture.
Using a mixer, cream the butter on medium speed for about 1 minute. Add both sugars and continue mixing on medium speed for 3 to 4 minutes, until the mixture is light and fluffy. Add the eggs and vanilla extract, mixing until fully incorporated. Scrape down the sides of the bowl, then reduce the mixer to low speed.
Add the flour mixture to the wet ingredients about a third at a time, mixing until just incorporated. Scrape down the sides of the bowl, then add the oats and raisins. Mix on low speed for 10 to 15 seconds – just enough to start combining. If needed, use a spatula to finish folding them in and ensure everything is evenly distributed. Chill the cookie dough for 30 minutes.
Preheat the oven to 350°F (175°C or 180°C). Line two cookie sheet pans with parchment paper. Using a medium cookie scooper, place twelve mounds of dough onto each sheet. Bake for 12 to 14 minutes, or until the edges are just beginning to turn golden. Be careful not to overbake – these cookies can become hard after a few days if baked too long.
Once you pull the cookies out of the oven, the tops will still feel soft but will firm up as they cool. Leave them on the pan for a minute or two, then transfer to a cooling rack to finish setting.