Cut each tomato into four thick slices; place on paper towels to drain. Meanwhile, in a small bowl, beat the cream cheese, parsley, basil, garlic and salt until blended. Spread cream cheese mixture over eight tomato slices; top with remaining tomato slices.
Place flour and bread crumbs in separate shallow bowls. In another bowl, whisk egg and milk. Coat the top and bottom of each sandwich with flour, dip into egg mixture, then coat with crumbs.
In a large skillet, heat the butter and oil over medium-hot heat. Fry tomato sandwiches in batches for 3-4 minutes on each side or until golden brown. Drain on paper towels. Serve immediately.