To make the brown butter sauce, melt the butter over medium heat. It will become foamy and then you will see brown specs. Gently swirl the butter in the pan. It will keep browning and smell nutty.
Fry the sage in brown butter. Use tongs to remove the leaves from the pan. Then take the butter off the heat.
While you do this, bring a large pot of salted water to a boil for the gnocchi.