Heat a large 12-inch saute pan over medium heat and add the oil. When hot, add the chaurice and saute, stirring occasionally until the sausage has rendered some of its fat and is lightly caramelized, 3 to 4 minutes. Add the garlic to the pan and saute for 30 seconds. Add the onions and peppers to the pan and continue to cook, stirring occasionally, until the onions and peppers are caramelized, about 5 to 6 minutes.
To serve, divide the sausage and peppers evenly among the hoagie rolls and serve immediately.