Preheat oven to 350°F and heat up the stove top griddle, or skillet, over medium.
Add some butter to the griddle and lay the sliced sub rolls down to toast; set aside.
Place the sausages on the griddle; cook until browned, about 5 minutes, turning often. Remove and set aside until cool to handle.
Next, add the peppers and onions to the griddle. Sauté and turn occasionally until softened. Season with a pinch of salt and cracked black pepper.
Slice the sausage and return to the griddle with the vegetables until heated through then transfer everything to a mixing bowl. Add tomato paste to the sausage and peppers and stir to glaze everything.
Place sausage and pepper mixture on toasted buns, top with cheese and a few sliced black olives (if using) then place into a hot oven for about 10 minutes until the cheese is melted.
Serve immediately.