To prepare sauce: Whisk water, peanut butter, rice vinegar (or white vinegar), soy sauce, honey, ginger and garlic in a small bowl.
To prepare tofu: Drain and rinse tofu; pat dry. Slice the block crosswise into eight 1/2-inch-thick slabs. Coarsely crumble each slice into smaller, uneven pieces.
Heat oil in a large nonstick skillet over high heat. Add tofu and cook in a single layer, without stirring, until the pieces begin to turn golden brown on the bottom, about 5 minutes. Then gently stir and continue cooking, stirring occasionally, until all sides are golden brown, 5 to 7 minutes more.
Add spinach, mushrooms, scallions and the peanut sauce and cook, stirring, until the vegetables are just cooked, 1 to 2 minutes more.
Ingredient note: Rice vinegar (or rice-wine vinegar) is mild, slightly sweet vinegar made from fermented rice. Find it in the Asian section of supermarkets and specialty stores.