Cut tofu crosswise into 1/2-inch-thick slices. Place tofu between paper towels until barely moist. Cut slices crosswise into 1/2-inch cubes.
Heat oil in a large nonstick skillet over medium-high heat. Add tofu; sauté 5 minutes, browning on all sides. Add peanut sauce; cook 2 minutes, stirring occasionally. Add sliced bok choy, squash, and onions; cook 3 minutes, stirring frequently. Add watercress and soy sauce; cook 1 minute or until the watercress is slightly wilted. Remove from heat.
Place 1 cup noodles in each of 4 shallow bowls; top each serving with about 1 1/4 cups vegetable mixture, and sprinkle with 1 tablespoon peanuts.