1/2 lb organic carrots, peeled & grated
2 tablespoons olive oil or grapeseed oil
1 1/2 pounds starchy potatoes or sweet potatoes
3/4 to 1 cup all-purpose flour, plus more as needed.
Heat the oven to 400 degrees. Bake potatoes until tender, about an hour. Immediately split them open to let the steam escape. When you can handle the potatoes, scoop out their flesh.
Cook in 2 tablespoons olive oil over medium-low heat, seasoning to taste, until very soft, 20 to 30 minutes.
Transfer to food processor and purée until smooth.
Bring a large pot of water to a boil and salt it. Pass potato flesh through a ricer or food mill, and season to taste. Stir the carrots into the mashed potatoes.
Sprinkle 1/4 cup flour on a clean counter or cutting board, and knead the potatoes with it, sprinkling in the remaining 1/4 cup flour, until the dough just comes together.
Pinch off a piece of the dough, and boil it to make sure it will hold its shape. If it does not, knead in a bit more flour (no more than necessary), and try again; the gnocchi will float to the top and look a little ragged when ready.
Roll a piece of the dough into a rope about 1/2-inch thick, then cut the rope into 1/2-inch lengths. Score each piece by rolling it along the tines of a fork; as each piece is ready, put it on a baking sheet lined with parchment or wax paper; do not allow the gnocchi to touch one another.
Add gnocchi to the boiling water a few at a time, and stir gently; adjust the heat so the mixture doesn’t boil too vigorously. A few seconds after they rise to the surface, the gnocchi are done; remove them with a slotted spoon or mesh strainer, and finish with any of the sauces below.