Whisk together ricotta, squash puree, egg, salt, and nutmeg.
Add flour and stir until mixture forms a soft ball; rest for 10 minutes covered.
Meanwhile, heat a large pot of lightly salted water to a boil. Melt butter in a large skillet over medium-low heat, add sage leaves and swirl pan around to crisp sage and allowing butter to brown evenly. Turn off heat and set aside.
Cut dough into six even portions and roll into a ½-inch log shape, using flour as necessary to keep from sticking. Cut logs into 1-inch pieces and set aside on a floured surface.
Drop gnocchi into boiling water in batches and cook until they float, about 3 minutes. Carefully strain cooked gnocchi.
Put the brown butter and sage pan back over medium-low heat and add cooked gnocchi. Heat through and serve promptly.
Enjoy!