Heat the olive oil in a large Dutch oven or soup pot over medium-high heat. Add the onion, pepper, mushrooms, and garlic. Cook until just tender and fragrant, about 3-5 minutes.
Add the cauliflower and water. Cover and simmer until the cauliflower is tender, about 5-7 minutes.
Uncover and add the ketchup, mustard, Worcestershire sauce, maple syrup, vinegar, and sriracha. Simmer, uncovered, until thick and bubbly, about 10-15 minutes.