Combine the flour and butter in a food processor. Process the ingredients until the butter is well combined. Add the eggs, 1 tablespoon of sugar and vanilla. Process the ingredients until a dough ball forms. Place in a zip-topped bag and refrigerate overnight or for a least 4 hours.
Preheat the oven to 375 degrees. Roll out 1/3 of the dough at a time on a well-floured board. Cut small circles and press the circles into mini-muffin pans. Repeat with the remaining dough.
Combine the pecans, ¾ cup sugar, 1/3 cup sour cream, and 1/8 teaspoon salt in a small bowl (the filling will be the consistency of thick paste). Place about 2 teaspoons of nut filling into each tart.
Bake the tarts for 18-22 minutes or until the edges start to brown slightly. Remove from the oven. Cool 15 minutes and then sprinkle with powdered sugar before serving.