For the crust:
1 1/4 cups all-purpose flour
1/4 cup cold vegetable shortening, cut into pieces
4 tablespoons cold unsalted butter, cut into pieces
1/2 teaspoon fine sea salt
3 to 4 Tbsp. ice-cold water
For the filling:
2 1/4 pounds very ripe tomatoes, thinly sliced
1 1/4 teaspoons kosher salt, divided
1 sweet onion, chopped
1 1/4 teaspoons freshly ground pepper, divided
1 tablespoon canola oil
1/2 cup assorted chopped fresh herbs (such as thyme, chives, parsley,and basil)
1/2 cup freshly grated Swiss cheese
1/2 cup freshly grated Parmigiano-Reggiano cheese
1/4 cup mayonnaise
Process first 4 ingredients in a food processor until mixture resembles coarse meal. With processor running, gradually add 3 Tbsp. ice-cold water, 1 Tbsp. at a time, and process until dough forms a ball and leaves sides of bowl, adding up to 1 Tbsp. more water, if necessary. Shape dough into a disk, and wrap in plastic wrap. Chill 30 minutes.
Preheat oven to 425°. Unwrap pie crust dough, and place on a lightly floured surface; sprinkle with flour. Roll the dough to 1/8-inch thickness.
Place the rolled out dough into a 9-inch pie plate. Trim dough 1 inch larger than diameter of pie plate; fold overhanging dough under itself along rim of pie plate, crimp a decorative edge, if desired. Chill 30 minutes or until firm.
Line piecrust with aluminum foil; fill with pie weights or dried beans. (This will keep the crust from bubbling up.) Place on an aluminum foil-lined baking sheet.
Bake at 425° for 20 minutes. Remove weights and foil. Bake 5 minutes or until browned. Cool completely on baking sheet on a wire rack.
For the filling:
Reduce oven temperature to 350°. Place tomatoes in a single layer on paper towels; sprinkle with 1 tsp. salt. Let stand 10 minutes. Meanwhile, sauté onion and 1/4 tsp. each salt and pepper in hot oil in a skillet over medium heat 3 minutes or until tender. Pat tomatoes dry with a paper towel. Layer tomatoes, onion, and herbs in the cooled pie crust, seasoning each layer with pepper (1 tsp. total). Stir together cheeses and mayonnaise; spread over the top of the pie.
Bake at 350° for 30 minutes or until lightly browned. If needed, shield the edges of the crust with foil to prevent excessive browning. Serve hot, warm, or at room temperature.