Heat 2 tablespoons olive oil in a large, oven proof dutch oven or stock pot. Add the chorizo and cook over medium high heat until browned. Remove with a slotted spoon to a plate with some paper towel on it to drain.
Season beef cubes with 1 tablespoon salt, 2 teaspoons pepper and 2 teaspoons smoked paprika. Add beef in batches to hot fat from chorizo and sear on all sides, about 3 – 5 minutes per batch. Remove to a separate plate and set aside.
Toss carrots and sliced onions with and additional 1 tablespoon salt, 2 teaspoons pepper and 2 teaspoons smoked paprika. Check to make sure there is enough fat to brown the onions and carrots. If not, add another tablespoon or two of olive oil. Add the carrots and onions to the fat and cook until they are caramelized (about 10 – 12 minutes). Add the garlic and cook about 30 seconds. Add the sherry and cook until almost completely evaporated. Put the chorizo and the meat (along with any accumulated juices) into the pot. Add the wine, beef stock, tomato paste, thyme and bay leaves. Bring to a boil, cover with a tight fitting lid and put in oven. Cook until meat and veggies are very tender (about 1 – 1 ¼ hours).
While stew is cooking, cook mushroom in 1-2 tablespoons olive oil in a large skillet over medium high heat until browned (about 10 – 12 minutes). Set aside.
Remove stew from oven when done and return to stove top over medium high heat. Remove thyme and bay leaves from stew. Create a slurry by combing cornstarch or arrowroot with 2-3 tablespoons of beef stock and mixing well. Stir into stew, cooking and stirring until thickened – it happens quickly. Add the frozen onions and mushrooms. Bring stew to boil then lower heat and simmer for about 10 minutes. Add the frozen peas and cook for another 5 minutes. Taste and adjust seasonings if needed.