Preheat the oven to 400°. Bake the potatoes for about 1 hour, or until tender. Halve the potatoes and scoop out the centers. Press the potato flesh through a fine sieve or a ricer into a large bowl. Season with the salt and pepper and let cool slightly. Make a well in the center, add the egg yolks and stir until combined. Stir in 1/2 cup of the flour. Turn the dough out onto a work surface and gently knead in the remaining 1/2 cup of flour, until the dough is smooth and no longer sticky. Wrap the dough in plastic and let stand at room temperature for 15 minutes.
Divide the dough into quarters and roll each piece into a 1/2-inch-thick rope. Cut the ropes into 1-inch lengths and dust with flour. To shape the gnocchi, hold a fork in one hand, tines pointing slightly downward, and use the thumb of your other hand to press the pieces of dough lightly across the back of the fork, rolling downward around your thumb to make an indentation around the outside.