Cabbage Pad Thai with Baked Tofu

Name: Cabbage Pad Thai with Baked Tofu
Ingredients: 3 tablespoons soy sauce, divided; 3 tablespoons grapeseed or olive oil, divided; 1 14-oz block extra-firm tofu, patted dry, cut into 1-inch cubes; 1 tablespoon fresh lime juice, plus more for serving; 2 tablespoons fish sauce; 1 tablespoon packed brown sugar; 1.5 teaspoons cornstarch; 1 cup thinly sliced onion (1 small onion); 7 to 8 ounces shiitake mushrooms, thinly sliced; 1 jalapeño, seeds removed, minced (about 2 tablespoons); 4 cloves garlic, minced; Kosher salt; 5 cups thinly sliced cabbage (about half a small head); 1/2 cup roughly chopped cilantro; 2 tablespoons roughly chopped peanuts