Arrange racks in upper and lower thirds of the oven. Preheat oven to 375 degrees. Line 2 large baking sheets with parchment paper.
Process pecans in a food processor until finely ground. Add flour, baking powder, cinnamon, and salt. Pulse to blend.
In a bowl, whisk together brown sugar, oil, and egg. Add to dry mixture in food processor, following by carrot. Pulse until just blended.
Spoon 8 slightly round tablespoons of dough onto each baking sheet, space evenly. Bake until cookies are springy to touch, about 10 minutes. Transfer rack and let cool.
Using an electric beater, stir together cream cheese, powder sugar, and vanilla. Pair cookies of similar shape and size. Spread filling evenly over flat side of one cookie in each pair, top with second cookie.
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