Place sausages in a large, nonstick pan in with an inch of water and a drizzle of oil. Bring to boil and let water evaporate; crisp and brown the sausage casings.
Meanwhile, heat another large skillet over medium-high heat with 2 tablespoons olive oil, 2 turns of the pan. Add peppers, onions, sliced garlic, oregano, salt and pepper. Cook to soften, 10-15 minutes. Add tomato paste and stir; add stock and reduce heat to a simmer.
In a small pan, heat remaining olive oil, about 2 tablespoons, with crushed garlic cloves. Melt butter into oil. Open and arrange rolls on a large baking sheet. Preheat broiler with the rack in the center of the oven. Lightly toast rolls, brush them with garlic butter, sprinkle with Parmigiano and parsley, and broil another 1 minute to set cheese.
Slice sausages lengthwise on the bias and combine them with peppers and onions. Fill garlic bread rolls a few slices of provolone and top with sausage, peppers and onions.