Soak 12 wooden skewers in water for at least 30 minutes.
Thread the beef, Brussels sprouts, mushroom and onions onto 12 skewers, alternating between meat and vegetables. Place in a large baking dish.
Preheat a grill or grill pan to medium-high heat.
Stir the olive oil, smoked paprika, oregano, garlic salt, coriander, lemon pepper and crushed red pepper in a large measuring cup. Reserve 1/4 cup of the mixture and pour the rest over the skewers.
Add the reserved marinade to a bowl with the sour cream, mayonnaise and lemon juice. Mix well until combined, then fold in the parsley and mint. Set aside until ready to use.
Carefully add the skewers to the grill and brush with the marinade. Cover and cook on one side for 3 to 4 minutes, then brush again with the remaining marinade and flip. Cook until the meat and vegetables are cooked to desired doneness, another 3 to 4 minutes. Remove to a platter and rest for 5 minutes. Serve with the creamy sauce.