Preheat the oven to 350°F. Place the pecans on a baking sheet and bake for about 6-8 minutes, until fragrant and lightly toasted. (Alternatively, you could toast the pecans in a medium skillet over medium heat for 5 minutes, stirring frequently.) Let them cool completely before using, about 15 minutes on the counter.
Place the toasted pecans and 2 tablespoons of the flour into your food processor or blender and process until they are finely ground. Set aside.
In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter, ¼ cup powdered sugar, and vanilla extract on medium speed until light and fluffy, about 2 minutes.
With the mixer on low, gradually beat in the remaining all-purpose flour and salt until fully combined.
Scrape down the sides of the bowl, add the ground nuts, and beat on low speed until combined.
Transfer the dough onto a piece of plastic wrap and flatten it into a medium disc. Wrap tightly with plastic wrap and refrigerate for 1 hour until chilled. (Alternatively, you could put the dough in the freezer for 40 minutes to speed up the process.)
Preheat the oven to 350°F and line two baking sheets with parchment paper.
Remove the chilled dough from the refrigerator and form it into 1-inch balls. I was able to make about 26 cookies.
Place them in a single layer onto the prepared baking sheets and bake for 12-15 minutes, or until the edges of the cookies start to brown. Remove them from the oven and place them on a wire rack to cool for 30 minutes.
Roll each cookie in the remaining 1 cup of powdered sugar to coat all sides. (The warmer the cookies, the more the powdered sugar turns into a paste, so don't rush the cooling process.)
Serve immediately or store in an airtight container for up to a week.
Notes
Don't have pecans? Try using a different nut like walnuts, almonds, hazelnuts, or pistachios!
To make this vegan, use your favorite non-dairy butter or margarine.
To make these ahead of time, follow all of the instructions and place the formed cookie dough balls in a freezer-safe bag or container and freeze. When you're ready to bake them, place them on two baking sheets lined with parchment paper and bake in a 350F oven for 15 to 18 minutes.