Melt 2 tablespoons of butter in a large skillet until fragrant and browned, about 3-4 minutes. Stir in the milk and 1 1/2 cups of water. Bring to a simmer, then add the polenta and cook, whisking constantly, until thickened, about 8-10 minutes. Stir in the cheddar, 1 tsp garlic powder, and a pinch of salt and pepper. Remove from heat and cover while you prepare the shrimp.
Dry the shrimp very well. In a bowl, toss the shrimp with the dried oregano, 1/2 tsp garlic powder, onion powder, cayenne pepper, black pepper, and a pinch of salt.
Heat 1 tablespoon olive oil in a skillet over medium. Cook the shrimp, in batches as needed, for 2-3 minutes per side. Toss in the remaining 2 tablespoons of butter, honey, garlic, and fresh oregano until fragrant, about 1-2 minutes longer.
Divide the polenta among bowls and top with the shrimp. Drizzle with any remaining sauce in the shrimp skillet and serve with fresh herbs, as desired.
Keyword dinner, hot honey, main course, pescatarian, polenta, shrimp, weeknight dinner