Preheat oven to 400°F.

Prick potatoes with a fork and wrap in foil.

Bake potatoes until tender, about 1 hour.

Let potatoes cool slightly, about 10 minutes.

Peel and cut potatoes into large chunks.

Rice the potatoes onto a work surface (about 6 cups).

Spread the potatoes into a 10x18-inch rectangle.

Top with egg yolks, flour, cheese, salt, pepper, and nutmeg.

Chop ingredients together with a pastry scraper.

Knead gently until dough forms a smooth ball.

Cut into 8 wedges and cover with a towel.

Dust baking sheets with flour.

Roll a wedge into a 3/4-inch-thick rope (18 inches long).

Cut the rope into 3/4-inch pieces and transfer to the baking sheet.

Repeat with remaining dough.

Refrigerate gnocchi for at least 30 minutes.

Grate tomatoes coarsely in a bowl; discard skins (about 1 3/4 cups puree).

Cook chorizo in a skillet, breaking up clumps, until browned (8-10 minutes).

Remove chorizo from skillet and set aside.

Heat olive oil in the skillet.

Add onion, salt, and pepper; cook until golden (5-7 minutes).

Add carrot and garlic; cook until softened (2 minutes).

Stir in tomato paste.

Deglaze skillet with white wine, scraping up browned bits.

Cook until wine reduces by two-thirds (3 minutes).

Return chorizo to the skillet with tomato puree, bay leaf, sugar, and chicken stock.

Bring to a boil, then simmer until sauce reduces by half (45 minutes).

Stir in cheese and oregano; season with salt and pepper.

Keep the sauce warm.

Cook gnocchi in batches in salted boiling water until tender (6 1/2 minutes per batch).

Gnocchi will float to the top after 1-2 minutes; continue cooking.

Transfer gnocchi to a warm platter with a slotted spoon.

Spoon chorizo sauce on top and garnish with cheese, oregano sprigs, and red pepper flakes.