Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1 ladleful pasta water.
While the pasta is working, position a rack 8 inches from the broiler and preheat to high. Broil the bell peppers, turning as necessary, until blackened all over, 12 to 15 minutes. Transfer to a bowl, cover and let cool for 5 minutes. Discard the peel and seeds. Using a food processor, puree the bell peppers for 30 seconds.
In a large skillet, heat 1 tablespoon EVOO, 1 turn of the pan, over medium heat. Add the sopressata and cook until crisp, 2 to 3 minutes. Transfer to paper towels to drain.
Add the remaining EVOO, 1 turn of the pan, to the skillet. Add the garlic and cook over medium heat for 2 minutes. Stir in the crushed red pepper, then the pureed roasted bell peppers. Stir in the tomatoes and oregano and heat through, 2 to 3 minutes. Stir in the reserved pasta cooking water. Add the pasta, parsley and cheese; toss. Top with the arugula and sopressata sticks.