Place tofu between several sheets of paper towels on a plate and top with another plate or heavy pan and let sit for 30 minutes to press out liquid. Discard towels and turn tofu block on it’s side and slice in half, making halves about 1 inch thick. Place slices in a pie plate or shallow baking dish.
In a small bowl, mix vinegar, sesame oil, 2 tbls soy sauce, honey, ginger, garlic and chili sauce. Pour this mixture over the tofu slices and cover with plastic wrap. Refrigerate for 2-4 hours, turning slices over halfway through.
Wash asparagus and snap off tough ends. Slice spears and tips into 1-inch pieces.
Remove tofu from marinade and pat dry. Save marinade.
Mix reserved marinade in a bowl with 1/4 cup soy sauce, lime juice, water and cornstarch.
Cut tofu slices into 1-inch cubes.
Heat oil over medium-high heat in wok or large skillet and stir-fry tofu until it begins brown, about 5 minutes. Remove tofu from pan to a plate.
Add asparagus, green onion and mushrooms to wok or skillet (add more oil if needed) and stir-fry until asparagus is just beginning to be tender, about 6 minutes. Return tofu to pan and stir-fry another minute or two.
Stir in marinade mixture and bring to a boil, cooking until slightly thickened. Serve at once over rice or noodles.