In the same pot, you will have a lot of brown bits on the bottom, add the chopped onion, carrots and celery. Cook the vegetables until soft, about 5 minutes, stirring occasionally.
Heat the olive oil in a Dutch oven over medium-high heat. Add the beef to the pot and cook just until the meat starts to brown. You will have to do this in 2 or 3 batches, since you do not want to crown the meat. Remove the meat from the pot after you're done and set aside.
Season the beef stew meat generously with salt and pepper. Place the beef in a ziploc bag and add the flour over the beef. Close the ziploc bag and shake until each piece of beef is fully covered in flour. Add more flour if needed.