Preheat the oven to 325°F (170°C, or gas mark 3).

The chopped pecans need to be finely chopped. You can either put them in a food processor for a few spins or you can place them in a resealable plastic bag and break them up with a kitchen mallet. Set them aside.

Place the powdered sugar in a shallow bowl and set aside.

In your large mixing bowl, combine the butter and sugar and beat them with an electric mixer on medium-high speed until light and fluffy. Stop the mixer and scrape the bowl. Add the vanilla and beat it until well mixed in.

Add the our and the pecans to the butter mixture and beat them in on low speed. Be sure to scrape the bowl once or twice. Once the flour is combined with the butter mixture, scrape the bowl and beaters.

Use a spoon to scoop 1-inch (2.5-cm) balls of dough. Roll them into round balls and place them 1 inch (2.5 cm) apart directly on a cookie pan. Bake for 16 to 18 minutes, or until lightly browned. Remove from the oven and let cool for 15 to 20 minutes before you roll them in the powdered sugar bowl, or the powdered sugar will melt and become gummy.