Rinse steaks (cold water) and pat dry. Place in ziploc bag and add red wine, dressing mix, and pepper. Squeeze air out and seal. Gently massage to combine ingredients and coat the steaks. Marinate for 2-3 hours.
Preheat grill to high heat (you will be grill these with direct heat). Lightly coat the grill grates with oil directly be grilling. In a bowl combine, mushrooms, bleu cheese, and Italian seasoning; set aside.
Remove steaks from bag. With a knife cut a pocket into the side of each steak, being carful not to cut through. Stuff steaks with the mushroom mixture and secure with toothpicks. Place on hot, oiled grill and cook for 5-7 minutes per side for medium. Remove from grill.
If you want to spruce it up, top with the oregano sprigs.