1) Prepare a grill to medium-high or preheat the broiler
2) In a small bowl or jar with a lid, whisk or shake together 3 Tb of the oil, the vinegar, and a pinch each of salt and pepper. Set the vinaigrette aside.
3) Toss the onion slices with the remaining 1 Tb of oil and wrap them tightly in 2 layers of foil.
4) Place the foil packet and the sausage on the grill or under the broiler. Cook both until the sausage is browned on both sides, sizzling, and heated through, 5 to 8 minutes per side.
5) Remove both from the grill and let them rest for 5 to 10 minutes.
6) Roughly tear the lettuce into bite-size pieces into a small bowl and dress it with the vinaigrette, tossing to coat. Set aside.
7) Being careful of escaping steam, open the onion packets and season very lightly with salt and pepper.
8) To make the sandwiches, cut the kielbasa into 6 lengths, then butterfly the pieces by slicing them lengthwise almost all the way through. On the bottom of each roll, layer the sausage, a slice of pineapple, a slice of onion, a slice of tomato, and a pile of the dressed lettuce. Drizzle over any leftover dressing or onion juices and top with the other half of the roll. Cut the sandwiches in half and enjoy.
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