In a 6-qt. dutch oven, heat 2 tbsp. EVOO over medium-high heat. Season the beef with salt and pepper, then toss with the flour to coat evenly. Working in batches, brown the beef on all sides, about 5 minutes per batch; transfer to a large bowl.
Add the carrots, onion, thyme, garlic and remaining 1 tbsp. EVOO to the pot and season with salt and pepper. Cover and cook over low heat, stirring occasionally, until slightly softened, 5 to 7 minutes. increase the heat to medium-high and stir in the tomato paste for 2 minutes. Add the broth and bring to a boil over medium-high heat. Add the beef and press a piece of parchment on top. Cover and cook over low heat, turning the meat once, until very tender, about 2 1/2 hours. ladle the stew into bowls and garnish with the pickled onions.