Pat the beef chuck cubes dry with paper towels and toss them with the all-purpose flour, salt, and black pepper until evenly coated.
Heat 1 tablespoon of olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the beef in batches until browned on all sides, then remove to a plate.
Add the remaining tablespoon of olive oil to the pot. Add the chopped yellow onion and cook until softened, about 5 minutes. Stir in the minced garlic and tomato paste, cooking for 1 more minute.
Pour in a splash of the beef broth to deglaze the pot, scraping up any browned bits from the bottom.
Return the browned beef to the pot. Pour in the remaining beef broth and add the fresh thyme. Bring the mixture to a boil.
Reduce the heat to low, cover, and simmer for 1 hour, stirring occasionally.
Add the potatoes and carrots to the pot. Cover and continue to simmer for an additional 45 to 60 minutes, or until the beef and vegetables are completely tender.
Remove from heat, taste and adjust seasoning if necessary, and serve hot.