In a mixing bowl, combine soy sauce, brown sugar, sesame oil, rice vinegar, gochujang, minced garlic, and grated ginger. Whisk until well mixed.
Add the cubed tofu and sliced shiitake mushrooms to the marinade, stirring gently to coat. Let it marinate while you prepare the vegetables.
Set the Instant Pot to ‘Sauté’ mode. Add the sliced onion and sauté for 2-3 minutes until it starts to soften.
Add the marinated tofu and mushrooms to the Instant Pot along with the marinated sauce. Stir to mix well.
Add the broccoli florets and julienned carrots to the pot. Stir gently to combine.
Close the Instant Pot lid and ensure the valve is set to sealing. Cook on Manual high pressure for 10 minutes.
Once cooking is complete, allow a natural release for 5 minutes, then switch to a quick release to release any remaining pressure.
In a small bowl, mix the cornstarch and water to create a slurry. Select the ‘Sauté’ mode again, and stir in the slurry to thicken the sauce, cooking for an additional 2-3 minutes while stirring.
Serve the vegan bulgogi over cooked rice and garnish with sesame seeds and chopped green onions.