- 3/4 to 1 lb whole smoked kielbasa or kosher salami
- 2 tablespoons olive oil
- 1 tablespoon Dijon mustard
- 1 tablespoon drained bottled horseradish
- 2 teaspoons white-wine vinegar
- 1 teaspoon honey
- 1/4 teaspoon salt
- 1/8 teaspoon black pepper
- 1 small head Boston lettuce, torn into small pieces
- 4 (6-inch-long) crusty rolls, such as Portuguese, halved horizontally
- Prepare grill for cooking. If using a charcoal grill, open vents on bottom of grill, then light charcoal. Charcoal fire is medium-hot when you can hold your hand 5 inches above rack for 3 to 4 seconds. If using a gas grill, preheat burners on high, covered, 10 minutes, then reduce heat to moderate.
- Cut kielbasa crosswise into 4 long sections, then halve each section lengthwise. If using kosher salami, cut lengthwise into 8 (1/4-inch-thick) slices. Trim off skin if desired.
- Whisk together oil, mustard, horseradish, vinegar, honey, salt, and pepper in a small bowl until emulsified. Toss lettuce with half of vinaigrette and reserve remainder.
- Grill tops and bottoms of rolls on lightly oiled grill rack, covered only if using a gas grill, turning over once, about 2 minutes total, then transfer, cut sides up, to a platter. Brush cut sides of top halves with remaining vinaigrette and mound salad on bottom halves.
- Grill sausage on lightly oiled grill rack, covered only if using a gas grill, turning over once, 3 to 4 minutes total, then arrange on top of lettuce (2 pieces per sandwich) and cover with top halves of rolls. Cut sandwiches in half crosswise.