For the red pepper sauce: In a blender or food processor, combine the red peppers (reserving 1 whole pepper or about 1/3 of the jar for later use), walnuts, tomato paste, smashed garlic cloves, fresh herbs, olive oil, vinegar, honey, smoked paprika, cayenne pepper, and a generous pinch of salt. Blend until smooth, approximately 1 minute.
Place a large pot with sides over medium-high heat. Add the butter, red pepper sauce, and 3 1/2 cups of water. Bring to a boil, then add the pasta. Season with salt and cook, stirring often, until the pasta is al dente, approximately 8-12 minutes. Do not drain the pasta water. If necessary, add additional water to ensure the pasta cooks properly.
Slice the reserved red pepper and add it to the cooked pasta along with the sun-dried tomatoes, grated Parmesan cheese, and chopped herbs. Toss until the pasta is well coated and creamy.
Arrange the burrata cheese in a serving bowl. Pour the hot pasta and sauce over the burrata, then gently toss to allow the cheese to melt into the pasta.
Serve the pasta topped with fresh Parmesan cheese, herbs, and chili flakes. Enjoy!