In a large skillet over medium heat, cook the ground beef, breaking it up with a spatula, until browned and fully cooked, about 5-7 minutes. Drain any excess grease.
Reduce heat to low and stir in 1 cup of marinara sauce. Simmer for 2-3 minutes, or until the mixture is heated through. Remove from heat and set aside.
In a medium bowl, combine the ricotta, parmesan, and Italian seasoning. Stir to combine. This will make about ½ cup of the ricotta mixture.
Spread ½ tablespoon of softened butter on one side of each bread slice.
On the unbuttered side of one of the bread slices, spread an even layer of the ricotta mixture (about 2 tablespoons).
Spoon about ⅓ cup of the ground beef mixture evenly over the ricotta mixture. Then, top with ¼ cup of mozzarella. Repeat with three more slices of bread.
Place one of the remaining bread slices on top of each sandwich, butter side facing up.
Heat a large skillet over medium heat. Working one or two at a time, place the sandwiches in the skillet. Cook for 3-4 minutes on each side, or until the bread is golden brown and crispy, and the cheese is melted.
Serve immediately with the remaining marinara sauce for dipping.