Preheat your oven to 400°F. Wash the potatoes and pierce them with a fork. Place on a baking sheet and bake for about 50 minutes, or until they are soft and easily pierced with a fork.
Allow the potatoes to cool enough to handle, then peel and mash them until smooth using a potato ricer or masher.
In a large bowl, combine the mashed potatoes, egg yolks, 2/3 cup gluten-free flour, and salt. Mix until a dough forms. If needed, add a little more flour at a time until it is easier to work with and less sticky.
Turn the dough onto a surface dusted with gluten-free flour. Knead gently until smooth, adding more flour as needed to prevent sticking.
Divide the dough into 4 pieces. Roll each piece into a long rope, about 1 inch thick. Cut into 1-inch pieces and roll each piece over a wooden gnocchi board or the tines of a fork to create ridges.
Bring a large pot of salted water to a boil. Cook the gnocchi in batches until they float to the surface, about 2-3 minutes. Cook for 1 minute longer. Remove with a slotted spoon and serve as desired.