Season steaks with salt and pepper, flour both sides and shake off excess. Add oil to a large skillet and turn to medium heat, add steaks. Brown the steaks on both sides and transfer to slow cooker. Add mushrooms to the top of the steaks.
Add broth to the skillet, whisking and scraping up all the browned bits at the bottom of the pan. Mix in the tomato sauce, thyme, and paprika then pour over steaks.
Cover and cook on low for 6 to 8 hours or high for 4 to 5 hours. Remove steaks to a serving plate. Stir the Greek yogurt and parsley into the liquid. Heat for another 10 minutes. Ladle sauce over steaks and serve!