Place flour in a small bowl; slowly add milk, stirring with a whisk until well blended to form a slurry. Add the broth and wine.
Heat oil in a large saucepan over medium-high heat; add onion and chicken. Sauté 2 minutes; stir in carrot and next 4 ingredients (carrot through pepper). Cover, reduce heat, and cook 4 minutes. Stir slurry into chicken mixture. Bring to a boil; cover, reduce heat, and simmer until thick (about 10 minutes), stirring occasionally.
Cut rolls horizontally 1 inch from tops. Hollow out bottoms of rolls, leaving 1/4-inch-thick shells; reserve torn bread and bread tops for another use. Spoon 1 1/4 cups chicken mixture into each bread shell.