Halve and thinly slice the shallot, thinly slice the garlic. Quarter the mushrooms. Cut the cauliflower into florets; discard stems. Cut the yellow squash into matchsticks. Small dice the ghost chili.
Heat the oil over medium heat in a saucepan, add the shallot. Stir occasionally until softened, about 2 minutes. Add the garlic, stir frequently until softened and fragrant, about 30 seconds.
Add the tomato sauces, cauliflower, mushrooms and squash. Bring to a low boil, stirring occasionally. Reduce heat to low and simmer for 30-50 minutes, or until cauliflower is soft.
Add the ghost chili and chili garlic sauce, stir until combined. Add salt and pepper to taste.
Divide portions into bowls, sprinkle with Asiago cheese. Tear and garnish with fresh cilantro and basil just before serving.