Heat 1 tablespoon of oil in a large saucepan and heat to medium. Add onions and cover. Cook for 10 minutes, stirring occasionally. Reduce heat to medium low and add garlic and 1 tablespoon paprika. Stir and cook for 1 minute.
In a food processor combine roasted red pepper and broth. Add to the pan along with the basil. Stir and scrape up browned bits. Increase heat to medium high and bring to a boil. Cook for 5 to 7 minutes, until thickened and most of the liquid has evaporated. Remove from heat and stir in yogurt, ¼ teaspoon salt and ¼ teaspoon pepper.
Meanwhile, combine beef, breadcrumbs, red onion, dried mustard, remaining ½ tablespoon paprika, ¾ teaspoon salt and ¼ teaspoon pepper in a medium bowl. Mix until just combined and form into 4 oval shaped steaks, about ¾ inch thick.
Heat remaining tablespoon of oil over medium high heat in a large skillet. Add steaks and cook until browned on the bottom, about 3 minutes. Turn, reduce heat to medium and cook until the other side is browned. Continue cooking and turning every 3 minutes, until an instant read thermometer registers 165 degrees. Serve with sauce.