First, wash and scrub the potatoes, then pierce them several times with a fork.
Place the potatoes on a microwave-safe plate and microwave on high for about 10 to 12 minutes, turning them halfway through, until they are fork-tender.
Alternatively, you can boil the potatoes until tender, but microwaving is faster.
Allow the cooked potatoes to cool for a few minutes, then peel the skin off. The potatoes should still be warm but cool enough to handle.
Using a potato masher or a ricer, mash the peeled potatoes until they are smooth and free of lumps. It is essential to do this while the potatoes are still warm for the best results.
Sprinkle the salt evenly over the mashed potatoes, and then add half of the flour. Gently mix the flour and potatoes until it starts coming together.
Gradually add the remaining flour, continuing to mix until a soft, slightly sticky dough forms. Avoid overmixing; you want the dough to be just combined.
Dust a clean surface with a bit of flour. Take a portion of the dough and roll it into a long rope, about ½ inch (1.3 cm) in diameter.
Use a sharp knife to cut the rope into 1-inch (2.5 cm) pieces. You can leave them as is or roll them gently over a fork to create ridges (this step is optional but traditional).
Bring a large pot of salted water to a boil. Carefully drop the gnocchi into the boiling water.
The gnocchi are done when they float to the surface, which should take about 2 to 3 minutes. Once they float, let them cook for an additional 30 seconds to 1 minute.
Use a slotted spoon to remove the cooked gnocchi from the boiling water and place them on a serving platter.
In a separate pan, heat olive oil over medium heat. Add the cooked gnocchi to the pan and sauté for a few minutes until they become lightly golden and crispy.
Season with salt and pepper to taste and garnish with fresh basil leaves.
Finally, serve your homemade vegan gnocchi hot with your choice of sauce, such as vegan tomato sauce or pesto, if desired.