Heat oven to 400°F. Place the ribs in a roasting pan or on a baking sheet in one layer. In a bowl, combine the garlic, oregano, cayenne, salt, and oil and mix well. Cover both sides of the ribs with the garlic and oregano mixture, coating evenly.
Roast in the oven for 1 hour flipping once after 30 minutes. Remove and let rest, covered, for 10 minutes. Reserve a fifth of the ribs (about 5 or 6 ribs) for another use.