The potatoes are cooked whole. My preferred method is to add 1 cup of water to the Instant Pot, set the potatoes on the rack, and cook on high pressure for 15-25 minutes depending on the size of the potatoes. See note if you don't have an Instant Pot.
Removed the cooked potatoes. Once they are cool enough to handle, peel the skin off with your fingers or a butter knife and discard.
Either pass the cooked potato through a ricer or pulse in a food processor (do not over process) to ensure there are no chunks. Transfer to a bowl and allow to come to room temperature.
Add the egg to the potatoes and mix to combine. In a separate bowl, combine both flours with the salt. Add small amounts of the flour mixture to the potato mixture and stir to combine. Once all of the flour has been added, use hands to gently knead the dough to mix but don't over work it. Knead it just to fully incorporate all of the ingredients. It will be incredibly sticky.
Lightly flour a work surface. Line a large baking sheet with parchment paper or a silicon mat and lightly sprinkle with flour. Grab a handful of the dough (use a large spoon since it is so sticky) and place on your floured surface. Sprinkle more flour on top of the dough to prevent sticking. Use the palms of your hands to start rolling the dough into a long rope that's about 3/4 inch wide. Use a dough cutter to cut the individual pieces of gnocchi that are about a 1/2 inch wide.
Transfer pieces to baking sheet but don't allow them to touch in order to prevent sticking. Lightly dust with more flour.
Repeat until you run out of dough, adding more flour to the work surface as needed. If you’re going to use the gnocchi within 2 to 3 hours, they can sit out on the counter. For longer storage, see the make ahead tips below.
My preferred method to cook gnocchi is to fry them. Coat the bottom of a fry pan with about a 1/4 inch of olive oil and heat over medium high heat. Add fresh for frozen gnocchi and fry until golden brown on all sides, turning as necessary. Drop 5-10 fresh sage leaves in the oil while they're cooking. Transfer to a paper towel lined plate to drain. Serve warm.
Notes
If you do not have an Instant Pot: You can put the unpeeled potatoes in a large pot, fill the pot with enough cold water to cover the potatoes by at least 2 inches and bring to a simmer over medium-high heat. Then reduce the heat to medium, partially cover the pot, and simmer the potatoes until they are completely tender and easily pierced with a skewer, 30 to 45 minutes. depending on the size of the potatoes.
You can serve freshly made gnocchi right away or within a couple of hours, or you can freeze them for later use. To freeze, put the gnocchi in the freezer while they’re still on the baking sheets and freeze until they are hard to the touch, at least one hour. Transfer them to a large plastic freezer bag and freeze for up to two months.
Cook frozen gnocchi in boiling water. You must do this in small batches as frozen gnocchi will cause the temperature of the cooking water to drop, so they’ll fall apart before the water returns to a boil if there are too many in the pot.
If you don't plan to cook fresh gnocchi within a couple hours, do not refrigerate. You must freeze. If refrigerated, they will release moisture and lose their shape.
You can use only all purpose flour, but you must fry them. Boiling makes them mushy.
If you want more of a chew or want to be able to boil them, double the amount of semolina flour and omit the all-purpose flour.