Preheat broiler. In a large saucepan cook peas in a small amount of boiling water 3 minutes. Using a slotted spoon, transfer peas to a bowl of ice water to cool quickly. Remove peas from ice water; drain well. Place asparagus in a steamer basket; place basket in saucepan over the boiling water. Cook, covered, 3 to 5 minutes or until asparagus is crisp-tender. Transfer asparagus to the ice water to cool; remove and pat dry with paper towels. Cut asparagus into 1/2-inch pieces.
In a food processor combine peas, beans, basil, 2 tablespoons of the lemon juice, 1 tablespoon oil, the paprika, and salt. Cover and process until nearly smooth.
In a bowl combine asparagus, cheese pieces, the remaining 1 tablespoon lemon juice, the 2 teaspoons oil, and the pepper. In a large nonstick skillet cook prosciutto over medium heat until crisp, stirring frequently.
Spread pea mixture on bread slices. Top with asparagus mixture. Broil 4 to 5 inches from heat about 2 minutes or until toppings are heated and cheese starts to melt. Top with prosciutto strips. If desired, sprinkle with cracked black pepper.