Cook peas according to package directions, substituting 1/2 cup broth for water. Drain; set aside in a serving bowl, and keep warm.
Cook prosciutto in a large skillet over medium-high heat until crisp. Remove prosciutto from pan; cool and coarsely crumble.
Melt 1 tablespoon butter with oil in large skillet over medium-high heat. Add onion; cook 28 minutes or until golden, stirring occasionally.
While onions cook, melt remaining 3 tablespoons butter in a small saucepan over medium-low heat. Cook 5 minutes or until butter is browned, stirring occasionally. Stir sugar, vinegar, thyme, and pepper into onion; cook 2 more minutes. Remove from heat. Stir caramelized onion and crumbled prosciutto into peas. Pour browned butter over peas. Serve warm.