Pierce the potatoes all over with a fork. Microwave the potatoes, turning once, until tender, about 12 minutes. Cut the hot potatoes in half and score the flesh to allow the steam to escape. Let the potatoes cool until cool enough to handle, then scoop the flesh into a ricer (see Cook's Note) and rice into a medium bowl. Spread evenly in the bowl to continue to allow the steam to escape. Discard the skins. Add the flour, salt and pepper and gently toss to combine. Form a well and add the egg. Starting in the center, mix well with your hand to combine. Place the dough on a clean counter dusted with flour. Knead the dough just until blended, 4 or 5 times.
Divide the dough into 4 equal pieces. Roll each piece with your palms on the work surface into a 1/2-inch-diameter rope (about 20 inches long). Cut the rope into 1-inch pieces. Roll each piece over a wooden paddle with ridges or over the tines of a fork to form grooves in the dough. Place on a well-floured surface. Continue with the remaining dough, dusting the gnocchi with additional flour as you go.
Cook the butter in a medium skillet over medium heat until it begins to brown, about 4 minutes. Remove from the heat. Add the thyme leaves. Set aside.
Bring a large pot of water to a boil. Season generously with salt.
Add the gnocchi to the boiling water and stir with a wooden spoon to prevent sticking. Cook until the gnocchi rise to the surface, about 1 minute. Continue cooking until the gnocchi are tender, 2 to 3 minutes longer. Using a slotted spoon, transfer the gnocchi to the hot thyme butter in the skillet. Toss to coat.
Spoon the gnocchi and butter sauce into shallow bowls. Top with the Pecorino and serve.
If you do not have a potato ricer, a food mill, potato masher or the back of a fork will work as well. Simply fluff the mashed potatoes before adding the flour to help prevent dense and gummy gnocchi.