Cook the polenta in the water or broth according to the package directions. Stir in 2 Tablespoons of the olive oil, cover, and set aside.
Heat the remaining 2 Tablespoons of olive oil in a lidded pan over medium heat. Sauté the mushrooms for 5 minutes, then add the garlic and cook for 1 minute.
In a small bowl, stir together the soy sauce, lime juice, water, and tomato paste. Pour it into the pan, bring to a boil, then cover and simmer for 10 minutes. Add more water as needed so the pan doesn't dry out.
Season the mushrooms with black pepper. If the polenta has thickened, stir in plant-based milk until creamy.
Spoon the polenta onto plates, top with the mushrooms, and serve right away.
Notes
Cook the polenta in vegetable broth for extra flavor.
No instant polenta? Regular polenta or coarse cornmeal works too. Simmer it over low heat, partly covered, whisking often, and plan on extra time.
Add the polenta to the liquid gradually while whisking to avoid lumps.
For gluten-free, use gluten-free soy sauce or coconut aminos and certified gluten-free polenta.