Preheat the oven to 400°F (200°C). Wash the potatoes, then use a fork or small knife to poke holes all over each one. Coat lightly with oil and salt, and roast directly on a baking sheet or oven rack for one and a half to two hours, or until fork-tender.

While the potatoes are still warm, scoop the flesh from the skins and pass it through a potato ricer onto a clean work surface, forming a mound.

Using a bench scraper, cut the mixture together, then gently knead it, adding one tablespoon of flour at a time until a smooth, pasta-like dough forms. Use as little flour as possible to keep the gnocchi light and tender.

Divide the dough into four equal pieces. Roll each piece into a one-inch (two and a half centimeter)thick rope, then cut into one-inch (two and a half centimeter) pieces to create pillow-shaped gnocchi.

Arrange the gnocchi on a floured, upside-down baking sheet and let them rest for 15 minutes.

Heat the butter and olive oil in a large sauté pan over medium heat until fragrant. Add the sage leaves and a large pinch of kosher salt, cooking until the sage is crisp. Transfer the sage to a paper towel-lined plate.

Bring a large pot of generously salted water to a boil. Add the gnocchi and cook until they float to the surface. Transfer them directly to the pan with the sage butter.

Add the lemon juice and increase the heat to medium-high. Cook, turning occasionally, until the gnocchi are golden brown and lightly crisp, about three to four minutes.

Add reserved pasta water one tablespoon at a time until a glossy, emulsified sauce forms. Stir in the lemon zest and toss to coat.

Divide the gnocchi among serving plates.

Top with the crispy sage, extra lemon zest if desired, and plenty of freshly grated Parmesan. Serve immediately.