In a large sauté pan, indoor grill or barbecue, cook the sausages until beginning to brown, about 5 minutes.
Arrange 4 bread slices on your work surface. Top each slice with a sausage link, 1 ounce of cheese, and half of a pepper. Season with salt and pepper. Top with remaining cheese and bread. Brush the sandwiches with oil.
Heat large nonstick skillet, Panini grill or indoor grill over medium heat. Add sandwiches and weight with a large dinner plate (if you are using a Panini grill, simply close the lid). Grill until bread is golden brown, then turn, weight with the plate and continue to grill until the second side is golden and the cheese has melted, about 5 minutes.
Transfer to a cutting board, slice in half and serve warm.
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