Preheat the oven to 220 degrees. Cut the peppers in half, remove the seeds and cut them again in two. Cover the baking dish with foil and place the peppers on it. Bake for about 30-35 minutes until the skin is black.
Remove the peppers from the oven and allow them to steam for a few minutes in a freezer bag. Remove the peppers from the bag and remove them from the peel. Place the peppers in a blender and puree them for about 20 seconds.
Cook the pasta according to the instructions on the package.
Heat the olive oil in a pan. Add the garlic and shallots and sauté for 2 minutes. Reduce heat to a lower setting and add the tomato paste and Tagatesse. Cook for another 2-3 minutes.
Add the basil and pureed peppers and simmer for 3-4 minutes. Add the vegetable stock and simmer for 2 minutes. Add salt if it's needed.
Serve pasta with the sauce. Garnish with Parmesan cheese and fresh basil.