Combine broth, sherry (or rice wine), soy sauce, 1 tablespoon cornstarch, sugar and crushed red pepper in a small bowl. Set aside.

Cut tofu into ¾-inch cubes and pat dry, then sprinkle with salt. Place the remaining 2 tablespoons cornstarch in a large bowl. Add the tofu; toss gently to coat. Heat 1 tablespoon oil in a large nonstick skillet or wok over medium-high heat. Add the tofu; cook, undisturbed, until browned, about 3 minutes. Gently turn and cook, stirring occasionally, until browned all over, 2 to 3 minutes more. Transfer to a plate.

Reduce heat to medium. Add the remaining 1 tablespoon oil, garlic and ginger; cook until fragrant, about 30 seconds. Add broccoli and water; cover and cook, stirring once or twice, until tender-crisp, 2 to 4 minutes. Stir the reserved broth mixture and add to the pan. Cook until the sauce has thickened, 1 to 2 minutes. Return the tofu to the pan; toss to combine with the broccoli and sauce.

Ingredient Note: Sherry is a type of fortified wine originally from southern Spain. Don't use “cooking sherry” sold in many supermarkets—it can be surprisingly high in sodium. Instead, get dry sherry that's sold with other fortified wines at your wine or liquor store.

People with celiac disease or gluten-sensitivity should use soy sauces that are labeled "gluten-free," as soy sauce may contain wheat or other gluten-containing sweeteners and flavors.