First, create the flavorful garlic butter spread. In a small bowl, combine the room-temperature butter, minced garlic, and dried basil. Mix them together until you have a smooth, consistent paste. This will be the foundation of your garlic bread.
Spread this mixture evenly on one side of each slice of soft Italian bread. Then, sprinkle the finely grated Parmesan cheese over the buttered sides. Gently press the cheese into the butter to help it adhere during cooking.
Bring a pot of salted water to a rolling boil. Add the angel hair pasta and cook it according to the package directions until it is al dente. Once cooked, drain the pasta thoroughly to remove excess water, which helps prevent a soggy sandwich.
In a separate bowl, stir the cooked angel hair pasta into the bolognese sauce. Make sure every strand is coated well. Using a thick sauce is important here, as it will hold together better inside the grilled cheese.
Lay one slice of the prepared bread on a clean surface with the buttered side facing down. Arrange three slices of mozzarella cheese on top, covering the bread from edge to edge. This cheese layer will create a barrier to keep the spaghetti contained.
Spread the bolognese-covered angel hair evenly over the mozzarella. Top the pasta with the remaining three slices of mozzarella cheese. Place the second slice of bread on top, this time with the buttered side facing up.
Heat a skillet over medium-low heat. You don't need to add any oil or butter to the pan, as the butter on the bread is sufficient. Carefully place the assembled sandwich in the hot skillet and cover it with a lid.
The key to a perfect grilled cheese is cooking it low and slow. This allows the bread to become golden and crispy while giving the cheese ample time to melt completely. Cook for about 5-6 minutes on the first side. Carefully flip the sandwich with a spatula, cover the pan again, and cook for another 4-5 minutes until the second side is golden brown and the cheese is fully melted and gooey. Serve it immediately while it's hot.