Fill a large pot with water, salt it thoroughly, and bring it to a boil. Cut larger sage leaves into smaller pieces; you can leave smaller ones whole.

When the water is almost boiling, heat a pan. Add the butter along with the sage to the hot pan and heat for a few minutes, stirring occasionally, until the sage is crispy and the butter is lightly browned and caramelized. Add the crushed garlic, salt, and pepper, then heat vigorously for another minute.

Once the water has boiled, add the gnocchi. As soon as they float to the surface, immediately remove them from the pot and add them directly to the buttered pan. Stir, sprinkle with finely grated Parmesan, and gently toss. The finished sauce should be shiny and velvety; if it's too thick, add a little of the gnocchi cooking water.