In a large Dutch oven, heat 2 tablespoons of olive oil over medium-high heat. Season beef chunks with salt and pepper, and brown on all sides for about 5-7 minutes.

Remove the beef and add diced onions, chopped carrots, and minced garlic to the pot. Sauté for about 4-5 minutes until softened.

Stir in 2 tablespoons of tomato paste, cooking for about 1 minute to deepen the flavor.

Pour in 1 cup of dry red wine, scraping the bottom of the pot and simmer for 3-4 minutes.

Add the browned beef back to the pot along with 4 cups of beef broth, bay leaves, thyme, parsley, mushrooms, and potatoes. Bring to a boil, then simmer for 1.5-2 hours.

In a mixing bowl, combine 2 cups of gluten-free flour with a pinch of salt. Create a well, then add 2 eggs and enough water to form a soft dough. Knead and let it rest for 10 minutes.

Roll out the dough into thin sheets and cut into noodle strips, dusting with flour.

Add the gluten-free noodles to the soup, cooking for 5-7 minutes until tender.

Ladle soup into bowls and serve hot, optionally with crusty gluten-free bread or salad.