For dressing: Puree red bell pepper, add vinegars and garlic. Add olive oil. Add salt and pepper, to taste, but keep in mind that arugula is peppery, so light on the pepper.
For Shrimp: Toss the shrimp with olive oil and minced garlic. Sear in a hot pan, until just cooked. Set aside.
Assembly: Place arugula on serving plate, drizzle with a little dressing, add shrimp, and top with pecorino romano and Parmesan. Drizzle with just a bit more dressing. Serve immediately.