Preheat the oven to 400 degrees F.

Prick the potatoes with a knife, and place on a baking sheet.

Bake in the oven until fork tender, about 60 minutes.

While the potatoes are baking, place the carrots in a saucepan and just cover with water.

Bring the water to a boil, then reduce the heat to medium and cook the carrots until they are tender, about 15 to 20 minutes.

Drain the carrots, puree them in a food processor until smooth, then place the pulp in a sieve over a bowl to drain out any excess liquid.

Once the potatoes are cooked, cool just until they are not too hot to handle, then cut in half.

Scoop out the pulp, then use a ricer, collecting two full cups of riced potatoes.

In a bowl, place the two cups of potatoes, ½ cup of the drained carrot puree, the two egg yolks, and some salt.

Mix with your fingers, then add the flour and stir just until a dough forms.

Dump the dough onto a lightly floured surface, and cut into 4 pieces.

Line a baking sheet with foil and lightly dust with flour.

Take a piece of the dough and using your hands roll into a ¾ of an inch rope. dusting with flour to prevent sticking.

Use a sharp knife to cut the rope into ¾ of an inch pieces and place on the floured baking sheet.

If desired, at this time you can roll each piece of dough against the tines of a fork to create ridges.

Once all the dough has been rolled and cut, store the tray in the refrigerator until ready to use.

Heat a large pot of salted water to a boil.

While the water is heating, place the butter in a small saucepan and melt.

Continue to cook the butter until it is just light golden brown.

Cook the gnocchi just until they rise to the surface, then drain.

Return the gnocchi to the pot, pour the browned butter on top and carefully toss to coat.

Serve the gnocchi into four individual bowls topped with grated Parmesan cheese and cracked black pepper.