Bring a large pot of salted water to a boil for the pasta. Meanwhile, melt the butter with the olive oil in a large skillet over medium-low heat, add the red onion, scallion, and salt and pepper to taste. Sauté until soft, about 15 minutes. Transfer to a blender and add the tarragon, basil, carrot juice, and yogurt and blend.

Cook the pasta in the boiling water until al dente, drain, and return to the pot. Gently mix in the sauce and adjust the salt. Transfer to heated bowls and top with the minced herbs and Parmesan.