Position the racks in the top and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment. Whisk together the flour, baking soda, cinnamon, salt and allspice in a large bowl.
Beat the butter, brown sugar and granulated sugar with an electric mixer on medium-high speed in a large bowl until light and fluffy, scraping down the sides of the bowl occasionally. Beat in the eggs 1 at time until blended, then beat in the vanilla.
Reduce the speed to low and beat in the flour mixture in 3 additions until smooth. Stir in the oats, raisins and walnuts with a rubber spatula. Drop heaping tablespoons of the dough onto the prepared sheets about 2 inches apart.
Bake the cookies, rotating the pans halfway through, until golden brown but still soft in the center, about 15 minutes. Let the cookies cool slightly on the baking sheets, then transfer to wire racks to cool completely. Store in an airtight container at room temperature for up to 3 days.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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