1. Preheat oven to 350°F. Into medium-sized bowl, measure flour, 6 tablespoons butter or margarine (3/4 stick), and 1/4 cup sugar; knead until well blended. Divide dough into 16 pieces. Press dough pieces into bottoms and up sides of sixteen 1 3/4-inch muffin-pan cups.
2. In 1-quart saucepan over low heat, melt 1 tablespoon butter. Remove from heat; stir in corn syrup, maple extract, and 1 tablespoon sugar, then stir in egg. Sprinkle chopped walnuts evenly into each pastry cup; spoon syrup mixture on top.
3. Bake cookies 20 to 25 minutes until crust is lightly browned and toothpick inserted in center comes out clean.
4. Cool cookies in pans on wire racks about 5 minutes or until firm. With tip of knife, loosen cookies from muffin-pan cups and place on wire racks to cool. Store in refrigerator.