Melt 1 tablespoon butter in a large saucepan over medium heat. Add carrot, sliced onion, shallots, sea salt, and ground black pepper, stirring to combine. Cover and cook 7 minutes, stirring occasionally.
Add water and peas; place lettuce leaves on top of mixture. Cover and cook 5 minutes or until peas are tender. Remove from heat; gently stir in 1 tablespoon butter.