Combine flour, Parmesan cheese, 1 tablespoon cilantro, and 1/4 teaspoon salt; cut in shortening with a pastry blender or fork until crumbly. Add 1/4 cup water, 1 tablespoon at a time, and stir with a fork until dry ingredients are moistened.
Shape dough into a ball, and press into a 4-inch circle over heavy-duty plastic wrap. Cover with more plastic wrap, and chill 15 minutes.
Roll dough, covered with plastic wrap, into an 11-inch circle. Remove plastic wrap, and fit dough into a 9-inch tart pan with removable bottom. Line pastry with aluminum foil, and fill with pie weights or dried beans.
Bake at 450° for 10 minutes. Remove weights and foil; bake 4 to 5 more minutes or until lightly browned. Cool on a wire rack.
Beat cream cheese at medium speed with an electric mixer until smooth. Add eggs, green onions, cumin, and remaining 1 tablespoon cilantro and 1/4 teaspoon salt, beating until blended. Spread evenly over crust.
Bake at 400° for 20 minutes. Cool on a wire rack 10 minutes.
Toss together avocado and lime juice. Spread pie with 1/2 cup sour cream, and sprinkle with Cheddar cheese, avocado, and tomato. Serve with salsa, if desired.