Make ravioli: Combine cheeses, chopped parsley, egg, 1/2 tsp. salt, and pepper in a medium bowl. Bring a large pot of salted water to a boil.
Lay 8 wrappers on a flat surface and spoon 1 tbsp. cheese mixture onto center of each. Working with 1 wrapper at a time, moisten edge with water and top with another wrapper, pressing to seal tightly. Transfer ravioli to a greased baking sheet, cover, and repeat to make more ravioli. Preheat oven to 250°.
Cook 4 or 5 ravioli at a time in boiling water until dough is tender, 3 minutes. Transfer to greased baking sheet in a single layer, cover with foil, and keep warm in oven.
Meanwhile, make sauce: Melt butter in a large frying pan over medium-high heat. Cook, swirling, until light golden, 3 minutes. Remove from heat; stir in lemon juice and parsley leaves. Layer ravioli and sauce on a platter.