Set a light-colored or stainless pan over medium heat. Add the butter and let it melt, then foam.
As the foam settles and color begins to build, add the sage leaves and smashed garlic clove.
Continue cooking, watching the color and smelling for a nutty aroma. Once the butter is amber and smells toasted, remove from heat immediately — it will continue cooking briefly off the burner. Lift the sage out onto a paper towel.
Meanwhile, bring a pot of salted water to a gentle boil. Add the gnocchi. When they float, they're nearly done; taste one about 30 seconds after floating to confirm, then remove with a slotted spoon.
Add the cooked gnocchi directly to the brown butter pan. Toss gently off the heat until glossy and coated.
Finish with a squeeze of fresh lemon and toss again.
Plate, spoon extra brown butter over the top, and finish with the crisp sage and grated Parmesan.
