In a large pot or Dutch oven, heat a bit of olive oil over medium heat. Add the diced onion and cook until softened.
Add the ground beef to the pot and cook until browned, breaking it up with a spoon as it cooks. Drain any excess fat.
Sprinkle the flour over the beef and stir to combine, allowing it to cook for 1-2 minutes to eliminate the raw flour taste.
Pour in the beef broth, stirring continuously to avoid lumps. Add the frozen peas and carrots to the pot.
Season the stew with kosher salt and fresh ground black pepper. Stir well to combine.
Bring the stew to a boil, then reduce the heat to low. Cover and simmer for about 15-20 minutes or until the vegetables are tender and the flavors meld.
Taste and adjust the seasoning if needed. If you prefer a thicker stew, you can let it simmer uncovered for a few more minutes.
Serve the hamburger stew hot in bowls. It pairs well with rice, mashed potatoes, or crusty bread.