Add the potatoes to a large pot of cool salted water. Bring to a boil and cook for 20-25 minutes or until fork tender. Drain and peel the potatoes. Then pass through a potato ricer.
Mix the flour and salt together then place on a clean/flat surface and make a well in the middle. Add the potatoes and egg, mixing together with your fingers to form a soft dough. It shouldn't stick to your fingers.
Add some more flour to the surface. Cut the dough into 6 equal pieces. Working with one piece of dough at a time, roll and stretch the dough until it forms a long skinny rope, about 1" thick. Cut about 1" wide gnocchi and then transfer to a baking sheet, making sure each gnocchi is covered in flour so they don't stick to each other.
In a large non-stick skillet, heat olive oil over medium heat. Add the pancetta and cook until it is crisp. Stir in the garlic and cook for another 30 seconds. Remove from heat and save any of the fat for the gnocchi.
In a large bowl, whisk together the eggs until there are no lumps and then add the cheese. Set aside.
Bring a large pot of salted water to a boil. Boil the gnocchi until they float, which should be about 3-4 minutes. Drain and reserve about ¼ cup pasta water.
With the same non-stick skillet over medium-high heat, add the gnocchi in a single layer. Cook for about 3 minutes until golden brown on bottom. Turn gnocchi and cook for an additional 3 minutes until golden brown.
Add the 2 tablespoon reserved pasta water to the egg mixture and mix to combine. Working quickly, add the gnocchi to the bowl with the egg mixture, and gently toss. Add remaining pasta water 1 tablespoon at a time until you reach desired consistency. Stir in pancetta and garlic and serve immediately.