Preparation

Make the dough

• Cover the potato with about 1 inch of water in a saucepan. Bring to a rolling boil over medium-high heat, reduce to a gentle boil, and cook until easily pierced with a skewer, 35 to 40 minutes. Drain and let cool briefly. Peel the potato as soon as you can handle it. Pass the potato through a ricer into a large bowl, spreading it out to help any steam escape.
• Melt 2 Tbs. of the butter in a large skillet over medium heat. Add the spinach and basil, and cook, stirring occasionally, until wilted and tender, 1-1/2 to 2 minutes. Let cool completely in the pan. Wring out the spinach in a clean kitchen towel, and finely chop. Transfer to a blender, add the eggs and yolk, and blend until combined.
• Add the spinach mixture to the still-warm potato and combine. Add the flour and 1 tsp. salt, and mix the dough gently with your fingers until it comes together. The dough should be soft but not sticky. Add more flour, 1 Tbs. at a time, if needed.

Shape the gnocchi

• Line 2 rimmed baking sheets with parchment and dust well with flour. Lightly flour a work surface. Turn the dough out onto the flour and gently flatten it by hand or by lightly rolling with a rolling pin until about 3/4 inch thick. If the dough is sticky, lightly dust the top with flour, too.
• With a floured bench scraper or a knife, cut the dough into strips from 1/2 to 3/4 inch wide. With your hands, roll and lengthen the strips until about 1/2 inch in diameter. Using the bench scraper, cut the logs into 1/2- to 1-inch pieces (size is up to you).
• If you want to give the gnocchi ridges, use the side of your thumb to gently roll each piece down the length of a gnocchi board or the tines of a fork, while simultaneously pressing lightly on the dough. (A fork will produce gnocchi with more pronounced ridges than a gnocchi board.)
• Arrange the gnocchi in a single layer on the prepared baking sheets, making sure they don’t touch. If not cooking the gnocchi right away, cover with plastic wrap and refrigerate for up to 4 hours. Even better, freeze the gnocchi right on the baking sheet until hard. (Frozen gnocchi are easier to handle than fresh and hold their shape better.)

Cook and serve the gnocchi

• In a small saucepan, melt the remaining 4 Tbs. of butter and keep it warm on the stove.
• Bring a large pot of well-salted water to a boil. Reduce the heat to just below the boil. Add the gnocchi and cook, stirring once, until they float to the surface, 1 to 3 minutes. Use a slotted spoon or similar utensil to transfer them to a bowl as they cook. Gently toss with enough melted butter to coat well, top with the grated cheese and black pepper, and serve immediately.

Make Ahead Tips

You can freeze the shaped, uncooked gnocchi for up to 1 month. Once frozen rock solid on the baking sheets, transfer them to freezer bags and return to the freezer. Cook as directed without thawing.