In a 12-inch skillet, melt the butter over medium heat. Add the onion and cook until softened, about 5 minutes. Add the edamame and cook for 3 minutes. Reserve 1 cup of the edamame; add the remainder to a food processor and puree with 1/4 cup cream, 1/4 cup water and a pinch each salt and pepper. Reserve the skillet.
Bring a large saucepan of salted water to a boil. Place the wrappers on a work surface and center a tablespoon of edamame mixture on each. Dampen the perimeter of a wrapper, fold into a half-moon shape and pinch the edge to seal. Place on a parchment-lined baking sheet. Repeat with the remaining wrappers. Add to the boiling water and cook until tender, about 5 minutes.
Meanwhile, in the reserved skillet, combine the reserved edamame, the remaining 3/4 cup cream and 1/4 teaspoon salt; bring to a boil. Add 1/3 cup of the ravioli cooking water and 1/3 cup parmesan; stir until the cheese is melted. With a slotted spoon, transfer the ravioli to the skillet; turn to coat in the sauce. Divide among 4 bowls and sprinkle with more parmesan.