Preheat oven to 350F. Split the dinner rolls in half lengthwise with a serrated bread knife. Following the manufacturer’s directions, heat the rolls in the oven until they are nicely browned, about 10 minutes.
While the bread is baking, heat the olive oil in a 10-inch skillet. Add the sliced onions, and sauté until very well caramelized, about 5 minutes.
Meanwhile, slice the sausage in half lengthwise, then cut each half into 4 smaller pieces. Place the sausage cut side down into the hot skillet (with the onions), and brown alongside of the onions for 3 to 5 minutes. Remove the onions and sausage from the pan and set aside, keeping them warm.
Remove the rolls from the oven. Separate the halves, and place them cut side down into the hot skillet, toasting them for 1 to 2 minutes, until the bread is toasty and brown. Fill with a piece of sausage, a pinch of grilled onions, and chimichurri sauce on the side.