Heat olive oil in a large pot over medium-high heat. Season short ribs with salt and pepper, then sear for 1-2 minutes on each side until golden brown.

Remove ribs, add butter, and sauté onions and carrots for 3-5 minutes until softened. Stir in garlic, thyme, and tomato paste until fragrant.

Deglaze with red wine, scraping brown bits. Add 2 cups beef stock and bay leaf, return ribs to pot. Cover and simmer for 3 hours.

Once ribs are tender, remove and shred meat, discarding bones. Return shredded meat to pot, add remaining 4 cups beef stock and simmer for 15 minutes.

In a bowl, combine cornmeal, flour, baking powder, baking soda, salt, and black pepper. Cut in butter until coarse crumbs form. Stir in milk and parsley.

Drop spoonfuls of dough into soup. Cover and cook dumplings for about 20 minutes until dry to touch and fluffy.

Ladle soup into bowls, ensuring each has dumplings. Garnish with chopped parsley before serving.