Melt butter in a large saucepan over medium heat. Add onions; cook 2 minutes, stirring frequently. Sprinkle flour over onions, and cook 1 minute, stirring constantly. Stir in milk and broth. Bring to a boil over medium heat, stirring constantly; cook 3 minutes or until slightly thick. Add peas; cook 5 minutes.
Place half of pea mixture in a blender. Remove center piece of blender lid (to allow steam to escape); secure lid on blender. Place a clean dishtowel over opening in the blender lid (to prevent spills). Process until smooth. Pour pureed pea mixture through a sieve over a large bowl, pressing mixture with a spatula. Reserve liquid; discard solids. Repeat procedure with remaining pea mixture. Stir in Mint Pesto, salt, and pepper; cover and chill. Garnish with mint sprigs, if desired.