Heat 2 tbsp sesame oil in a large skillet over medium high heat. Place tofu cubes into pan with at least 1/4 inch between them - you can do this in batches, too, if the pan isn't large enough. Sear on one side for 3-4 minutes, then flip and cook an additional 3-4 minutes until both sides are crispy and brown. Sprinkle 2 tbsp soy sauce (1 tbsp if doing 2 batches, save the second tbsp for the second batch) and let tofu caramelize for about 2 minutes. Remove from pan and set aside on a plate.
While tofu cooks, prepare the sauce. Whisk 1/2 cup soy sauce, brown sugar, corn starch, and water or broth in a bowl. Set aside.
Add 1 of the remaining tbsp of sesame oil into the pan or into a wok if you have one, over high heat. Toss half of the cut veggies and cook until slightly softened but still crunchy. Add half of the garlic (3-4 cloves) and cook an additional 30 seconds until fragrant. Pour half of the sauce over and bring to a brief boil, stirring constantly until sauce thickens and coats the vegetables. Remove from pan and repeat with the remaining veggies.
To portion: add tofu amount of choice (3-4 squares most likely if you cut them thick) to a container along with about 1 cup of vegetables and 1/2-1 cup of cooked rice, if desired. When serving, garnish with sesame seeds, cilantro, and lime juice as you wish.