Spread tofu on paper towel–lined baking sheet, let drain for 20 minutes, then gently press dry with paper towels. (Tip: Freezing then defrosting the tofu in its original package allows for easier release of the liquids as described after draining.).
Working in batches, use food processor fitted with slicing blade to process mushrooms, carrots and pepper until thinly sliced; set aside. Process bok choy in now‐empty processor until thinly sliced; set aside.
Fit again‐empty processor with chopping blade and pulse tofu until coarsely chopped, about 5 pulses, stopping to redistribute tofu as needed. Line baking sheet with clean paper towels, spread tofu on sheet and press gently with more paper towels to dry. Transfer tofu to bowl and toss with 2 tablespoons cornstarch.
Pulse ginger and garlic in again‐empty processor until finely ground, about 8 pulses. Transfer ginger mixture to small bowl and stir in 1 teaspoon vegetable oil. Whisk soy sauce, sherry, sugar, sesame oil, orange zest and juice, and remaining 1 tablespoon cornstarch together in separate bowl.
Heat 2 tablespoons vegetable oil in 12‐inch nonstick skillet over high heat until just smoking. Add tofu in single layer and cook, breaking up any clumps with wooden spoon, until well browned, 8 to 10 minutes; transfer to bowl.
Heat remaining 2 teaspoons vegetable oil in now‐empty skillet over high heat until just smoking. Add mushrooms, carrots, and bell pepper and cook, stirring occasionally, until spotty brown, about 4 minutes. Push vegetables to sides of skillet. Add ginger mixture and cook, mashing mixture into skillet, until fragrant, 15 to 30 seconds. Stir ginger mixture into vegetables.
Add bok choy and cook until just wilted, about 1 minute. Whisk sauce to recombine, then add to skillet along with tofu. Cook, tossing constantly, until sauce is thickened, about 30 seconds. Off heat, sprinkle with peanuts and scallions. Serve over rice.