Wash and cut cauliflower head into quarters, then trim off and discard leaves and thick stem. Using a box grater or food processor, coarsely grate cauliflower.

Place cauliflower, broth, polenta, and salt in a medium saucepan. Stir and bring to a boil over high heat. Cover and reduce heat to medium-low; cook, stirring occasionally, until polenta is soft and the mixture has thickened, 10-12 minutes.

Preheat a large skillet over medium-high heat. Once the skillet is hot, add butter and swirl to coat the bottom.

Add zucchini and corn to the skillet; cook, stirring occasionally, until vegetables are lightly browned and softened, 5-7 minutes.

Meanwhile, combine garlic powder, onion powder, salt, and pepper in a medium bowl. Add shrimp and toss to coat.

Add shrimp to the skillet with the veggies; cook until opaque, 4-5 minutes. Pour the BBQ sauce into the skillet and toss to combine.; remove from heat.

Add cheese and 2 Tbsp butter to the pan with the cauliflower grits and stir until melted and well combined. Remove from heat.

To serve, divide cauliflower grits between plates or bowls. Top with vegetables and shrimp.