Preheat an outdoor grill for cooking over medium-high heat.
Brush the cut-side of each baguette half generously with olive oil and sprinkle with salt. Grill until charred and nicely toasted, about 5 minutes. Remove from the heat and set aside.
Grill the soppressata until it blisters and curls slightly, 1 to 2 minutes per side.
Rub the cut-side of the garlic halves over the cut-side of the grilled bread. Then do the same with the tomato halves, pressing firmly until only the tomato skins are left.
Cut both the grilled soppressata and tomato skins into bite-size pieces and transfer to a medium bowl. Add the, mint, parsley, vinegar, remaining tablespoon olive oil and a sprinkle of salt and toss to combine. Cut each bread half on a bias into 6 even pieces. Top each piece of grilled bread with the tomato-soppressata mixture.
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