Preheat the oven to 450°F (232°C). Wash the potatoes and pierce them all over with a fork. Wrap them in aluminum foil and bake for 1 hour, or until soft.
Remove from the oven and foil, allow to cool for at least 5 minutes before handling. Cut each potato in half crosswise, then carefully peel off the skins. You can do this with your fingers or a spoon, but be careful because the potatoes will still be hot.
Place the peeled potatoes in a large bowl. Use a potato ricer or masher or the back of a fork to mash the potatoes until very smooth. This is important because the potatoes need to be broken down as much as possible.
Slowly pour in ½ cup (60g) of the flour and the salt and mix with a fork until shaggy pieces form; then begin to knead the dough with your hands. Add the remaining flour in ½-cup (60g) increments, kneading after each addition to work in the flour, until you have a dough that is soft but no longer sticky or tacky. (See note, about gnocchi dough above for more help if this is your first time making gnocchi.)
Turn the dough out onto a clean, lightly floured surface and shape it into a small loaf around 6 inches long. Cut the loaf into 5 equal pieces.
Use your hands to roll a piece of the dough into a log thats 15 to 19 inches in length and about 1 inch in diameter. Cut the log crosswise into 1-inch pieces for the gnocchi. Sprinkle a rimmed baking sheet with flour.
Take piece of dough and roll it into a ball. If you like, use the back of a fork to press down gently and create the ribbed effect shown in the photos. . Place the formed gnocchi on the prepared baking sheet and cover with a clean kitchen towel. Repeat with the remaining 4 pieces of dough until all are made.
Prepare the pesto by adding all ingredients into a food processor or blender and blend until smooth. Taste and adjust any seasonings to preference. If you do not like pesto too garlicky just use 1 clove.
Bring a large pot of salted water to a boil. Drop the gnocchi into the boiling water in batches (about 10 to 20 gnocchi at a time) and cook for 3 to 5 minutes, or until they float to the top.
Once they float to the top place the cooked gnocchi in a pan with 2 to 3 tablespoons of the pesto and a few tablespoons of pasta water. Keep adding in the gnocchi as they cook.
Once they are done taste an add any salt or vegan parmesan if desired, enjoy.