Egg-roll wrappers make these a snap to prepare.
Melt 1 tablespoon butter in a medium skillet over medium heat. Add chickweed, deadnettle, and wild garlic greens and cook until bright green and softened, about 2 minutes. Transfer to a food processor and pulse until finely chopped. Season with a pinch each of salt and pepper. Transfer to a medium bowl and fold in ricotta and Parmesan with a rubber spatula. Let cool.
Place 9 wrappers on a work surface. On each wrapper, mound 4 separate teaspoonfuls of filling in a grid 2 inches from edges. Dip a finger in water and trace a circle around each mound of filling. Place remaining 9 wrappers on top; press to seal. Cut out 36 ravioli with a 2-inch ring cutter.
Bring a large pot of salted water to a boil; add oil. Cook ravioli until al dente, 5 to 8 minutes. Drain well. Serve topped with remaining 2 tablespoons melted butter and a sprinkling of Parmesan and garlic greens.