Preheat the broiler and char the red cherry and bell peppers until evenly blackened. Place in a bowl and cover to cool. Peel and seed the peppers. Finely dice the red cherry peppers, and then chop the red bell peppers into 1/4-inch dice.
Meanwhile, heat the EVOO in a large Dutch oven over medium-high heat and add the pancetta to render, 2 to 3 minutes. Stir in the mushrooms and cook until dark and tender, 12 to 15 minutes.
Add the rosemary, sage, thyme, marjoram, garlic, onions and some salt and black pepper and cook 5 minutes. Stir in the tomato paste and roasted peppers. Deglaze with the wine and cook until reduced by half, scraping reducing up the bits on the bottom of the pan, about 2 minutes. Stir in the tomatoes and simmer gently, stirring occasionally, until the tomatoes break down, 30 minutes.
Bring a large pot of salted water to a boil and cook the pappardelle to al dente. Reserve 1 cup of the starchy cooking water before draining, and tossing the pasta with the sauce and the cooking water 1 minute. To serve, combine the pasta with lots of grated pecorino, passing more at the table, for topping.
For a make-ahead meal, cool and store the ragu. Reheat over medium heat, cooking the pasta right before serving.