Heat oven to 350°. Set a wire rack on a rimmed baking sheet. Lay prosciutto on rack. Bake until crisp, about 20 minutes.
Whirl bell peppers, yogurt, 1/4 tsp. kosher salt, and the pepper in a food processor until blended. Add more salt to taste to dressing if you like.
Open pita halves carefully and coat each half with about 2 tbsp. dressing (reserve remaining dressing for another use).
Divide eggs, avocado, and arugula between pita halves. Wedge a prosciutto slice inside each pocket.
Note: Nutritional analysis is per pita half.