Heat the olive oil in a skillet over medium heat. Add the garlic and cook just until sizzling and fragrant, about 1 minute. Add the pepper to the oil and remove from heat; transfer pepper mixture to food processor work bowl along with basil, vinegar, cayenne and bread crumbs. Puree until smooth and season to taste with salt and pepper.
Heat oven to 450 degrees. Slice polenta into 1/2-inch thick rounds and arrange on parchment-lined baking sheet. Drizzle 2 teaspoons oil over the rounds and sprinkle with the cheese. Bake until golden brown, 12 - 15 minutes.
Serve warm topped with about 1/2 teaspoon of red pepper rouille and a basil leaf.