In a stand mixer, beat flour, sugar, and salt on low speed to blend. Add shortening in spoonfuls and beat on low speed until pieces are pea-size, about 1 minute. Add butter and beat until pieces are pea-size, stopping once to scrape bowl, about 2 1/2 minutes. Gradually drizzle in 5 1/2 tbsp. ice water, beating just until dough comes together, 15 to 30 seconds.
Divide mixture in half and gently gather and press each into a 3/4-in.-thick disk. Wrap each in plastic wrap. Chill until firm, at least 2 hours and up to 2 days.
Unwrap 1 pastry disk and lightly flour pastry, work surface, and rolling pin (save remaining disk for another use). Working from center with short strokes, roll pastry into an even 12-in. circle. As you work, lift pastry using a bench scraper or long metal spatula, and reflour board and pin as needed to keep it from sticking.
Fold pastry in half and open up into a regular 9-in. pie pan, easing it into place without stretching. Using scissors, trim overhang to 1 in.
Roll overhang under itself so it's flush with and sitting on top of rim. Pinch pastry along lip to form an even ridge. Flute ridge. Wrap with plastic wrap and freeze until firm, 30 to 40 minutes.
Bake blind: Preheat oven to 400° with a rack in lower third. Line pastry with foil, letting ends come straight up from pan but not over rim. Fill with pie weights or dried beans. Bake until crust is golden at edges, 20 to 25 minutes. Remove foil and weights. If needed, bake until center is dry, 2 to 5 more minutes.
Make ahead: For dough, up to 2 days, chilled or 1 month, frozen. For blind-baked crust, up to 1 day, airtight.