Preheat the oven to 350°F and line 2 large cookie sheets with parchment paper.
Beat wet ingredients (4 min): In the bowl of a stand mixer, or in a large bowl with an electric mixer, beat the butter, sugar, and brown sugar on medium-high speed until light and fluffy, 2-3 minutes. Add the eggs and vanilla and beat until combined, 1 minute.
1 cup unsalted butter, 1/2 cup granulated sugar, 1 cup light brown sugar, 2 large eggs, 2 teaspoons vanilla extract
Mix dry ingredients (2 min): In a separate medium bowl, whisk together the flour, baking soda, cinnamon, ginger, cardamom, all spice, salt, and oats.
1 3/4 cups all-purpose flour, 1 teaspoon baking soda, 1 1/2 teaspoons ground cinnamon, 1 teaspoon ground ginger, 3/4 teaspoon ground cardamom, 1/2 teaspoon ground all spice, 1/2 teaspoon salt, 3 cups quick oats
Combine (2 min): With the mixer on low speed, slowly add the dry ingredients until combined. The dough will be sticky.
Scoop (5 min): Using a medium cookie scoop, or 1.5 Tablespoons (about 35g each if you’re weighing them), drop the dough 2-3 inches apart on the prepared baking sheet.
Bake (10-12 min): Bake in the preheated oven for 10-12 minutes, until the edges are golden and the tops are just set (they should still look very soft). Allow the cookies to cool on the baking sheet for 10 minutes then transfer to a wire rack to cool completely. The filling will melt if you try to frost/sandwich warm cookies.
Make the filling (5 min): In a large bowl with a hand mixer or stand mixer fitted with the paddle attachment, beat the butter on medium speed until smooth. Add the powdered sugar and beat for 2-3 minutes, until light and fluffy. Pour in the eggnog (or milk) and vanilla and beat for another 1-2 minutes. Taste and add salt as needed.
1/2 cup unsalted butter, 3 cups powdered sugar, 2 Tablespoons eggnog, 1 1/2 teaspoons vanilla extract, kosher salt to tast
Sandwich the cookies (5 min): Spread about 1 Tablespoon of frosting on the bottom of half of the cookies or pipe with a piping bag. Sandwich with another cookie right side up. Store in an airtight container at room temp for 2 days or in the fridge for up to 4 days.