Combine chicken broth, salt, and pepper in a large Dutch oven; bring to a rolling boil. Add shelled peas, celery, and onion; return to a boil. Cook, uncovered, 20 minutes or until peas are tender. Strain through a food mill into a large bowl. Process vegetables, discarding vegetable pulp. Return vegetable mixture to Dutch oven, and set aside.
Melt butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add whipping cream; cook over medium heat, stirring constantly, until thickened and bubbly.
Gradually stir reserved vegetable mixture into cream sauce. Heat thoroughly. (Do not boil.) Serve immediately in individual soup bowls; garnish with chopped parsley.