Preheat the oven to 300 degrees.
Put the pecans and 2 tablespoons of the granulated sugar in a food processor fitted with the metal blade. Finely grind the pecans and set them aside.
Put the butter and the remaining 4 tablespoons of granulated sugar in the bowl of an electric mixer. Using the paddle attachment, cream the butter on medium speed for 2 or 3 minutes, until light and fluffy.
Add the vanilla extract. Combine the flour and salt and stir into the butter mixture.
Add the reserved nuts.
Form the dough into ¾-inch balls. Line a baking sheet with parchment paper and put the cookies on the pan, 2 inches apart.
Bake the tea cakes for about 20 minutes, until light brown. While they are still warm, sprinkle them with the powdered sugar.