Don’t rush processing the cauliflower; it’s key to giving the puree the consistency of grits. You can also use purchased riced cauliflower. If it’s frozen, you can toss it right into the saucepan unthawed.
Process half of the cauliflower in a food processor until very finely chopped. Transfer to a medium saucepan. Repeat with the remaining cauliflower. Add stock and cornmeal to pan; bring to a boil over high. Cover and reduce heat to medium-low; simmer, whisking often, until cauliflower is cooked and mixture is thickened, about 10 minutes. Remove from heat. Stir in cheese, pepper, and salt. Cover to keep warm.
Combine tomato sauce, 3 tablespoons water, mustard, ketchup, garlic powder, chile powder, and onion powder in a small saucepan. Bring to a simmer over medium. Simmer, stirring often, until slightly thickened, about 6 minutes. Stir in shredded chicken. Divide cauliflower mixture among 4 bowls. Top evenly with chicken mixture. Sprinkle with scallions.