Place the tomatoes in a large nonstick skillet over medium-high heat. Cook, shaking the pan occasionally, until the tomatoes are tender and the skins are charred in spots, about 15 minutes. Set aside to cool.
Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, 8 to 10 minutes. Drain and place in a large serving bowl.
For the vinaigrette: Place the tomatoes, basil, vinegar, olive oil, honey, smoked salt, and pepper in a blender. Blend until smooth.
Pour the vinaigrette over the pasta and toss until coated. Sprinkle with Parmesan cheese. Season with smoked salt and pepper, to taste, and serve.