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.
Place the tomatoes, basil, vinegar, olive oil, honey, smoked salt, and pepper in a blender. Blend until smooth.
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.
Pour the vinaigrette over the pasta and toss until coated. Sprinkle with Parmesan cheese. Season with smoked salt and pepper, to taste, and serve.