Bring a large pot of salted water to a boil and keep it ready while you start the sauce.

Heat olive oil in a large Dutch oven over medium heat. Add the shallots and sauté for about 2 to 3 minutes until golden and fragrant.

Stir in the red bell peppers, thyme, oregano, and rosemary. Season generously with salt and pepper. Cook for 15 to 18 minutes, stirring occasionally, until the peppers are soft and caramelized.

Add the minced garlic and balsamic vinegar. Cook for about a minute until the vinegar reduces slightly and the garlic becomes aromatic.

Pour in the vegetable stock and bring to a gentle simmer. Let it cook for 5 minutes while the pasta begins cooking.

Drop the linguine into the boiling water and cook it for one minute less than the package instructions for an al dente texture.

Remove the herb stems from the pot, stir in the heavy cream, and transfer the mixture to a high-speed blender. Blend until the sauce is smooth and silky, about 90 seconds.

Drain the pasta and return it to the pot. Pour the creamy red pepper sauce over the pasta, add the grated parmesan cheese, and toss over low heat until everything is well coated and the cheese has melted.

Stir in the chopped parsley. Plate the pasta and top with torn burrata cheese. Drizzle with a little olive oil and sprinkle extra parmesan and herbs on top if desired.