Heat oven to 350°F (325°F for dark pan). Grease 36 mini muffin cups with shortening; sprinkle lightly with flour. In medium bowl, break up cookie dough. Stir or knead in 2 tablespoons flour until well blended.
Divide dough into 36 pieces. Shape each piece into ball; place in muffin cup. With thumb, make indentation in center of each.
Bake 6 to 8 minutes or until light golden brown. Meanwhile, in medium bowl, beat egg. Stir in brown sugar, butter, corn syrup and vanilla until well blended.
Remove pan from oven. With back of measuring teaspoon, make indentation again in each partially baked cookie. Spoon about 1 teaspoon pecans into each cookie; top each with about 1 teaspoon brown sugar mixture.
Return to oven; bake 8 to 12 minutes longer or until edges are golden brown. Cool in pan on cooling rack 5 minutes. Run knife around edge of each cookie to loosen; cool 1 to 2 minutes longer. Remove cookies from muffin cups; place on cooling racks to cool.