Using tongs, pull the ribs from the pan juices, and transfer to a clean, rimmed baking sheet. Try to keep the bones attached to the ribs for aesthetics. Pour pan juices through a mesh strainer into a clean bowl. Reserve the solids (carrots, onions, garlic, etc.). Skim fat from the pan juices, then pour back into the large pot. Add reserved vegetables. Warm over medium-high heat until boiling, then cook for 10 minutes until the mixture begins to thicken. Using a fork, mash 1 tablespoon of butter with the flour in a small bowl until well combined. Whisk the butter-flour paste into the juices, then simmer until the sauce coats the back of a spoon (about 5 minutes longer). Season to taste with kosher salt and black pepper.