Heat 2 teaspoons olive oil in a medium saucepan over medium heat. Add garlic and onion, and cook until translucent, about 4 minutes. Sprinkle with flour, and stir to coat. Add chicken stock, tomato sauce, vinegar, paprika, and red-pepper flakes. Bring to a boil, and reduce to a simmer. Let cook until slightly thickened and aromatic, about 30 minutes. Set aside, and keep warm.
Meanwhile, cook the potatoes: Heat oven to 375 degrees. Cut the potatoes in half lengthwise. Toss in a bowl with remaining teaspoon olive oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper.
Place the coated potatoes cut side down in a single layer on a large cookie sheet, and bake until golden brown and cooked through, about 35 minutes. Remove from oven, and serve with reserved warm tomato sauce, garnished with chopped oregano.