Position a rack about 6 inches below the heat source of your broiler. For most ovens, this will be one notch below the top shelf. Set the oven to broil and allow 5 minutes to preheat fully while you cook the onion and meat.
Heat oil in a large (12-inch) skillet over medium-high heat until shimmering. Add the onion and sauté, stirring occasionally, until softened, about 2 minutes. Add ground venison, Italian seasoning, salt, pepper, and garlic powder. Cook, breaking up the meat into small pieces using a wooden spoon or spatula, until cooked through, about 5 minutes.
Meanwhile, split the 4 English muffins in half. Toast in a toaster until golden brown, about 3 minutes. Place cut-side up on a parchment-lined rimmed baking sheet.
Add marinara or pizza sauce to the cooked meat, stir until well combined, and remove from heat. Divide the meat and sauce mixture between the toasted English muffins.
Sprinkle with the shredded cheese.
Broil in the oven until the cheese is melted, 1 to 2 minutes. Let cool for 3 minutes before serving.