Wash Swiss chard thoroughly. Remove and chop stems. Slice leaves into (1-inch) strips.
Place peas in a large Dutch oven; cover with water to 2 inches above beans. Bring to a boil; cook 5 minutes. Drain peas; set aside. Wipe pan with a paper towel.
Heat oil in pan over medium-high heat. Add onion; sauté 2 minutes. Add tomato paste and garlic; cook 1 minute, stirring constantly. Stir in peas and broth; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until peas are tender. Stir in chard stems and cheese; cover and cook 4 minutes. Stir in chard leaves, oregano, salt, and pepper; cover and cook 2 minutes. Stir in lemon juice.