Preheat oven to 450 degrees Farenheit. Whisk flour, 1/2 teaspoon salt and pepper in a shallow dish. Dredge turkey in the mixture; discard any extra flour mixture.
Heat oil in a large ovenproof skillet over high heat. Add the turkey; cook until golden brown on one side, 3-5 minutes. Turn the turkey over and transfer pan to over. Roast until the turkey is just cooked through, no longer pink in middle, 15-20 minutes. While turkey is in oven, prepare your green beans to your liking; steamed is great way!
Once turkey is done, transfer to a plate and tent with foil to keep warm.
Place the turkey skillet over medium heat. (taking care to handle properly since handle will still be hot!) Add shallots and thyme and cook, stirring constantly, until the shallots begin to brown, 30 seconds to 1 minute. Add blueberries, vinegar and remaining 1/4 teaspoon salt; continue cooking, stirring occasionally and scraping up any brown bits, until the blueberries burst and release their juices and the mixture becomes thick and syrupy, 4-5 minutes. Slice the turkey and serve with blueberry pan sauce with green beans.