Bring a large pot of water to a boil with a few large pinches of salt. Once boiling, add in the potatoes.
Cook for 10-15 minutes. Then drain through a strainer and let the potatoes cool down for 10 minutes.
Use a potato masher to mash the boiled potatoes until smooth. Let the mashed potatoes cool for another 5 minutes before adding the flour.
On a clean surface, place the mashed potatoes and sprinkle with the flour and salt. Gently mix the ingredients in to form a dough. If it feels sticky, add a bit more flour as needed.
Knead the dough gently for about 2-3 minutes until it comes together. Make sure not to over mix it.
Roll the dough into a long log (about 1-inch in diameter). Using a sharp knife, cut the log into small bite-sized pieces. For the traditional gnocchi shape, gently roll each piece over the tines of a fork to create ridges.
Bring a large pot of salted water to a boil. Drop the gnocchi into the boiling water in small batches, making sure not to overcrowd the pot.
Keep a bowl ready to add the hot gnocchi into.
Once they float to the top (in about 2-3 minutes), use a slotted spoon to remove them and place in the bowl. You might have to do it in batches, depending how big the pot is.
Once all the gnocchi is ready, place a large saucepan over medium heat. Add in the 1 tbsp of olive oil.
Once hot, evenly add the gnocchi into the pan. Let it cook and crisp up for a few minutes, flipping over to cook both sides.
Add the pesto in, making sure to coat all the gnocchi. Let it cook for another minute per side. Then remove from the heat and serve hot!