Add vegetable oil to a large, heavy-bottomed pot or deep skillet. Heat over medium heat until the oil reaches 325°F-350°F. Use a thermometer to monitor the temperature.
In a shallow bowl, whisk together flour, steak seasoning, baking powder, baking soda, salt, and pepper.
In a separate shallow bowl, whisk together buttermilk and egg.
Pat cube steaks dry with paper towels. Dredge each steak in the seasoned flour, dip into the buttermilk mixture, then dredge once more in the flour mixture, pressing gently so the coating adheres.
Set breaded steaks aside for a few minutes to allow the coating to set.
Carefully lower steaks into the hot oil, working in batches so you don't overcrowd the pot. Fry for approximately 3-5 minutes per side, until golden brown and cooked through. Check the internal temperature with a meat thermometer.
Transfer cooked steaks to a wire cooling rack or paper towel-lined plate to drain. Repeat with the remaining steaks.
To make the gravy, melt butter in a saucepan over medium heat.
Add garlic and fresh thyme. Cook for about 1 minute until fragrant.
Whisk in flour and cook for another minute.
Slowly pour in beef broth while whisking constantly to prevent lumps. Continue stirring until the gravy thickens.
Stir in heavy cream and season with salt and pepper to taste.
Serve country fried steak warm with plenty of gravy over mashed potatoes.