In a bowl, combine the drained and cubed tofu, garlic, thyme, 1 tablespoon oil, salt and pepper. Cover and let stand for 20 minutes.
To a large heated skillet, add the tofu and marinade and cook till lightly browned. Transfer to a plate.
In the same skillet, heat 3 tablespoons oil and add the onions. Cook for 3-4 minutes. Add the mushrooms and cook another 2 minutes. Next add the asparagus and snow peas and cook for 2 minutes. Pour in the wine and vegetable broth.
In a measuring cup, blend the cornstarch with 2 tablespoons of water; add water to make 1/3 cup. Pour cornstarch mixture into the skillet, bring to a boil, and continue to cook until veggies are tender. Add salt and pepper to taste. Sprinkle tofu over the top.