Divide cheese slices between half of bread slices. Sprinkle each evenly with Italian seasoning, oregano, and salt. Brush edges of bread with beaten egg and top with remaining bread slices. Press edges to seal and trim crusts.
Add milk to remaining egg, whisking until combined.
In a large skillet, heat oil and butter over medium heat.
Lightly coat bread evenly with flour. Working in batches of 2, dip into egg mixture, letting excess drip off. Place in skillet and cook until golden brown, 2 to 3 minutes per side. Sprinkle with more salt. Serve warm.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/mozzarella-toasts/