Make the basil aioli. Combine all the ingredients in a small food processor and blend until smooth. Season to taste with salt and pepper and refrigerate until ready to use.
Preheat an oven to 425 F.
Preheat a baking sheet. The key to this recipe is preheating a baking sheet in the oven for 10-15 minutes before topping with the sausages, peppers, and onions to really get that sizzle.
Combine sausage, peppers, and onions. In a mixing bowl, toss the sausages, peppers, onions, and garlic with the olive oil, oregano, red wine vinegar, salt, and pepper. Once the baking sheet is hot, carefully spread the sausages and other ingredients in a single layer.
Bake. Return the baking sheet to the oven and bake for 20 minutes, flipping the ingredients halfway through. If the sausages, peppers, and onions need a little more color, switch the broiler on for 3-5 minutes. Remove the sheet pan from the oven.
Toast the buns. While the sausages are in the oven, spread the sides of the buns with softened butter and toast in a nonstick skillet until golden brown.
Assemble. Layer a sausage with peppers and onions in a toasted bun, add chopped Calabrian chilies, and drizzle with the basil aioli. Serve right away.