Mix rosemary, garlic, and olive oil in a bowl. Rub standing rib roast with mixture and season liberally with kosher salt and black pepper.
Heat an 11-inch cast-iron skillet over medium-high heat until skillet is very hot. Brown standing rib roast on all sides in the hot skillet, 3 to 5 minutes per side. Remove meat from skillet. Cook and stir carrots, celery, and onions in the hot skillet until slightly browned; stir beef broth into vegetables. Place roast on top of vegetables in skillet.
Roast meat in the preheated oven until an instant-read meat thermometer inserted into the middle reads 120 degrees F (49 degrees C), about 2 1/2 hours.
Transfer roast from skillet to a serving platter, retaining pan drippings and vegetables; let rest at least 30 minutes before slicing.
About 15 minutes before serving, combine red wine with dried cherries in a saucepan over medium heat; bring to a boil and reduce heat to low. Simmer until cherries have absorbed all the wine, about 10 minutes, stirring occasionally; remove from heat.
Melt butter in a separate saucepan over medium heat and whisk flour into hot butter to make a paste. Strain reserved pan juices into cherries using a fine mesh strainer. Bring cherry sauce with pan juices to a boil. Stir flour paste into sauce, reduce heat to low, and simmer until thickened, about 5 minutes. Season sauce with salt and black pepper. Serve sauce with roast.