In a large bowl, combine the beef stew meat and flour. Stir and toss to ensure the beef is evenly coated. This step is crucial as the flour helps thicken the stew during cooking.
Heat the unsalted butter in a large Dutch oven or pot over medium-high heat. Swirl the pan or stir it to ensure the butter melts completely and coats the bottom of the pot.
Once the butter is melted, add the coated beef chunks to the pot. Sear the meat for about 5 minutes, flipping it intermittently to ensure even browning on all sides. After searing, remove the beef and set it aside on a plate.
Add the red onion to the Dutch oven and sauté for about 5 minutes, stirring frequently until the onions start to soften and turn translucent.
Next, add the garlic and sauté for an additional minute, just until it's fragrant. Stir constantly to avoid burning the garlic.
Deglaze the pot by pouring in the beef broth, using a wooden spoon to scrape up any browned bits from the bottom. This adds incredible flavor to your stew.
Stir in the tomato sauce and tomato paste, mixing well to combine everything.
Return the seared beef to the pot, along with the celery, carrots, potatoes, salt, and pepper. Stir to combine all the ingredients.
Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let the stew simmer for about 90 minutes, stirring occasionally. This long, slow cooking time helps develop rich flavors and tender meat.
After the meat is tender and the vegetables are cooked through, taste the stew and adjust the seasoning with more salt and pepper if needed. If the stew is too thick, you can add more beef broth or water to reach your desired consistency.