1. To prepare crust, weigh or lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 1 teaspoon sugar, and 1/2 teaspoon salt in a medium bowl; cut in 3 tablespoons butter and shortening with a pastry blender or 2 knives until mixture resembles coarse meal. Sprinkle surface with ice water, 1 tablespoon at a time; toss with a fork until moist and crumbly (do not form a ball). Press mixture gently into a 5-inch circle on plastic wrap; cover. Chill 1 hour.
2. Preheat oven to 375°.
3. Unwrap dough. Roll into an 11-inch circle on a lightly floured surface. Fit dough into a 9-inch tart pan with a removable bottom. Press dough against bottom and sides of pan. Chill in freezer 10 minutes.
4. Line bottom of dough with a piece of foil; arrange pie weights or dried beans on foil. Bake at 375° for 15 minutes or until edge is lightly browned. Carefully remove pie weights and foil; bake an additional 7 minutes or until center is lightly browned. Cool 1 minute on a wire rack.
5. To prepare filling, combine quince paste and 1 tablespoon juice in a food processor; process until smooth. Spread quince mixture evenly over warm tart shell. Bake at 375° for 15 minutes or until filling is bubbly. Reduce oven temperature to 350°.
6. Combine remaining 1 teaspoon juice, 1/4 cup sugar, honey, and 1/8 teaspoon salt in a small saucepan over medium heat. Bring to a boil, stirring until sugar dissolves. Boil 2 minutes. Remove from heat; carefully add 2 tablespoons butter, stirring until butter melts. Stir in nuts. Pour nut mixture over quince paste. Carefully spread evenly. Bake at 350° for 10 minutes or until topping bubbles. Cool 1 hour on a wire rack.