Preheat oven to 350°F In a large zip top bag, toss beef with flour, salt and pepper. Heat 1 tbps olive oil in a 5-qt Dutch oven Brown beef in 3 batches, transferring to a plate as they're done. Add 1 tbsp more oil to pot for each batch.
When all the beef is browned, add 1 tbsp more oil to the pot. When it shimmers, add the diced onion. As the onion gives up its juices, scrape up the browned fond on the bottom of the pot. When onion is soft, about 3 minutes, add garlic. Stir until fragrant, 1-2 minutes. Stir in tomato paste and cook, stirring frequently, until tomato begins to brown and films the bottom of the pot.
Return beef (and any accumulated juices) to pot. Add potatoes, carrots, broth, beer, bay leaves and thyme. Season with salt and pepper. Cover and bring to a boil, stirring occasionally.
Transfer pot to oven and cook, covered, 2 hours. Add mushrooms and pearl onions, recover and return to oven. Continue cooking, covered, until meat is tender, 30-60 minutes more. Stir in peas. Adjust seasoning and remove bay leaves before serving.