Cut beef roast into small 1-2 inch, bite size pieces.
Season the beef with salt and pepper.
Sprinkle flour onto the beef pieces and toss to coat.
Heat the butter in the dutch oven over medium high heat.
Once the butter is melted and the pot is hot, add half of the beef pieces.
Sear the beef on all sides. Remove the seared beef to a plate and cover with foil to keep warm.
Continue searing the second half of the beef pieces. Once all the beef is seared, keep covered on a plate until the vegetables are sauteed.
If the pot is dry, add another tablespoon of butter. Add onions, carrots, celery, and garlic. Sautee until onions are slightly tender.
Deglaze the pot with the pinot noir. Stir and scrape the bottom of the pan to remove any brown bits and incorporate that flavor into the soup. Simmer for 2 minutes to slightly reduce the pinot noir.
Add the tomato paste, beef broth, smoked paprika, bay leaf, sea salt and black pepper.
Stir, reduce heat to medium low, cover and simmer for 3 hours, stirring occasionally.
After 2 hours of simmering, add the peas to the soup. Cover and continue to simmer.
Once the beef is fork tender, mix the tapioca flour and water in a small bowl. Pour the mixture into the soup and stir.
Add the potato gnocchi to the soup, stir, and cook for an additional 4-5 minutes.
Serve immediately with a warm slice of sourdough bread.
Beef and gnocchi soup can be refrigerated in an airtight container for up to 5 days.