Heat the sesame oil in a large skillet over medium heat. Add the garlic and cook until starting to brown, about 1 minute. Add the shiitake mushrooms and stir until well coated with oil. Cook for about 4 minutes, stirring occasionally.
Mix in the zucchini and cook until the zucchini is cooked through, for 4 more minutes. Add the bean sprouts, most of the basil (reserve some for garnish), and season with salt and pepper, to taste. Mix well until the basil is wilted. Stir in the desired amount of sriracha.
Serve over brown rice. Sprinkle with sesame seeds and basil. Squeeze lime juice over the dish, and eat up!