Pat the beef chuck roast cubes dry with paper towels and season generously with salt and pepper. Heat olive oil in a large heavy-bottomed Dutch oven or pot over medium-high heat until shimmering, about 2 minutes.
Working in batches to avoid crowding, brown the beef on all sides until deeply caramelized, 3-4 minutes per batch. Transfer browned meat to a clean plate and set aside; don't worry about cooking it through since it will finish during the simmer.
Reduce heat to medium, add diced onion to the pot, and sauté until softened and fragrant, about 4 minutes. Stir in minced garlic and cook for another minute, then add tomato paste and stir constantly for 2 minutes to caramelize the paste slightly.
Pour in beef broth and tomato sauce, scraping the bottom with a wooden spoon to release all flavorful browned bits. Return the beef to the pot along with bay leaves, thyme, and rosemary, stirring well to combine everything evenly.
Bring the mixture to a gentle boil, then reduce heat to low, cover partially, and simmer for 45 minutes until the hearty savory beef stew begins to thicken naturally. The broth should bubble gently at the edges but never vigorously boil.
Add sliced carrots and cubed potatoes, stir gently, and continue simmering uncovered for 20-25 minutes until vegetables are fork-tender. Mix cornstarch with water to create a slurry and stir it in during the final 2 minutes if you prefer a thicker consistency.
Taste and adjust seasoning with additional salt, pepper, or herbs as desired. Remove bay leaves before serving in deep bowls with crusty bread on the side for soaking up every delicious drop.