Recipe from The Craft of Baking
3/4 cup old-fashioned rolled oats
Preheat the oven to 350˚F. Line two baking sheets with parchment paper.
Grind the oats in a food processor or blender to make a fine flour. In a medium bowl, whisk together the oat flour, all-purpose flour, cinnamon, nutmeg, baking soda, and salt.
In a bowl of an electric mixer fitted with the paddle attachment, beat the butter, brown sugar, granulated sugar, and vanilla extract on medium speed until well combined. Add the egg and beat to combine, scraping down the sides of the bowl with a rubber spatula. With the mixer on the lowest speed, add the dry ingredients in two additions, scraping down the sides of the bowl after each one. Add the carrots and mix until just to combine. The dough will be very sticky.
Drop 1-tablespoon mounds of the dough onto the prepared baking sheets, spacing them 1/2 inch apart. Bake, rotating the sheets once halfway through, until the cookies are golden brown and spring back when gently touched in the center, about 12 minutes. Cool the cookies completely, on the baking sheets set on a wire rack, before filling.
To make the filling, in the bowl of an electric mixer fitted with the paddle attachment, beat the cream cheese, butter, lemon zest, sugar, and salt on medium speed until well combined, scraping down the sides of the bowl as needed. (The filling can be kept in a covered container in the refrigerator for up to 1 week. Let it come to room temperature before using.)
Using a small spoon or spatula, spread 1 teaspoon of the filling over the flat side of half of the cookies. Sandwich with the remaining cookies, flat sides together.
The cookies can be kept in an airtight container for up to 2 days.