1. To prepare crust, weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour and 1/4 teaspoon salt in a food processor; pulse 2 times or until combined. Add 1/4 cup chilled butter; pulse 4 times or until mixture resembles coarse meal. With processor on, add ice water through food chute, processing just until combined (do not form a ball).
2. Preheat oven to 425°.
3. Press dough gently into a 4-inch circle on plastic wrap. Cover and chill 20 minutes. Slightly overlap 2 sheets of plastic wrap on a slightly damp surface. Unwrap and place chilled dough on plastic wrap. Cover with 2 additional sheets of overlapping plastic wrap. Roll dough, still covered, into an 11-inch circle. Place dough in freezer 5 minutes or until plastic wrap can be easily removed.
4. Remove 2 sheets of plastic wrap; let stand 1 minute or until pliable. Fit dough, plastic-wrap side up, into a 9-inch pie plate lightly coated with cooking spray. Remove remaining plastic wrap. Press dough into bottom and up sides of pan; fold edges under and flute. Line pastry with foil; place pie weights or dried beans on foil. Bake at 425° for 15 minutes or until lightly browned. Remove weights and foil. Reduce oven temperature to 350°. Bake crust an additional 5 minutes or until pastry is golden. Remove pan from oven, and cool on a wire rack.
5. To prepare filling, melt 2 tablespoons butter in a large skillet over medium-high heat. Add asparagus to pan. Sprinkle 1/4 teaspoon salt and 1/8 teaspoon pepper over asparagus; sauté 8 minutes or until crisp-tender, stirring frequently. Add onions; sauté 2 minutes or until asparagus just begin to brown. Remove from heat. Spoon asparagus mixture into prepared shell in an even layer. Arrange goat cheese in an even layer over asparagus mixture.
6. Combine eggs, egg yolk, and milk. Stir in remaining 1/4 teaspoon salt, remaining 1/8 teaspoon pepper, and nutmeg. Pour custard into pie plate. Bake at 350° for 30 minutes or until quiche is almost set in the center. Remove from heat, and cool 5 minutes on a wire rack before slicing.