Pat beef dry with paper towels—moisture prevents browning. Heat 3 tablespoons olive oil in a large Dutch oven over medium-high heat until shimmering, approximately 3 minutes. Working in batches, sear beef until deep mahogany brown on all sides, 6–8 minutes total per batch.
Remove beef to a clean plate. Add diced onion to the pot and cook 5 minutes, stirring frequently until edges soften. Add minced garlic and cook 1 minute until fragrant.
Stir in tomato paste and cook 2 minutes, allowing it to deepen in color and develop concentrated sweetness. This step is essential because raw tomato paste tastes acidic and thin.
Add chili powder, cumin, and paprika, stirring constantly for 1 minute. Pour in diced tomatoes with their juice and beef broth, scraping the pot bottom to release browned bits. Return beef to the pot along with the bay leaf.
Bring the hearty beef chili to a gentle boil, then reduce heat to low. Cover partially and simmer 35–40 minutes, stirring occasionally. Beef should be fork-tender with almost no resistance when pierced.
Add chopped bell peppers, sliced carrots, and drained kidney beans. Simmer uncovered 10 minutes until vegetables soften slightly but maintain texture. Season with salt and black pepper, adjusting to taste.
Ladle into bowls and serve immediately, or cool completely before refrigerating for deeper flavor development overnight. The best beef chili stew tastes even better the next day as flavors meld.