Separate the gnocchi and pat away any surface moisture. Prepare the sage, Parmesan, garlic, lemon zest, and lemon juice.
Heat the olive oil in a 12-inch light-colored stainless-steel or enameled skillet over medium heat. Add the gnocchi in a mostly single layer and cook for 4 to 5 minutes, turning occasionally, until golden on several sides.
Carefully add 3 Tbsp water and cover immediately. Cook for 2 minutes. Uncover and cook for another 2 to 3 minutes, until the water evaporates and the centers are tender. Season with kosher salt and pepper, then transfer to a plate.
Reduce the heat to medium-low. Remove any scorched crumbs with a heatproof spoon, then add the butter and sage. Cook, swirling frequently, for 2 to 4 minutes, until the milk solids are amber-brown and the sage is crisp.
Remove the skillet from the heat. Stir in the garlic for 20 seconds, followed by the lemon zest and juice.
Return the gnocchi to the skillet and toss to coat. Fold in the Parmesan and serve immediately with the crisp sage leaves, extra Parmesan, and optional flaky salt.