For the meatball sliders:Preheat the oven to 350 degrees F. Halve individual dinner rolls; set aside.
In a large bowl, combine beef, egg, salt, pepper, garlic powder, parmesan, and chopped basil. Mix until all ingredients are well blended. Shape mixture into 12 golf ball-sized meatballs; set aside on a plate.
Set a large pan to medium-high heat. Once hot, add meatballs and cook 1-2 minutes per side, then flip. (They do not need to be fully cooked at this point.) Remove meatballs to a paper-towel lined plate; drain excess fat in pan.
Pour marinara sauce into the pan and place meatballs in the sauce. Cook for 8-10 minutes, flipping meatballs occasionally, until sauce has reduced to a thick consistency. Remove from heat.
Place one meatball inside each halved dinner roll. Top with sliced mozzarella, then cover with dinner roll top. Place on a large baking sheet.
For the garlic butter:In a small bowl, combine butter, garlic, basil, and parmesan, stirring until evenly mixed. Pour garlic butter mixture over top of the sliders. Bake for 15-20 minutes, until the rolls are golden brown and cheese is melted. Cut into individual sandwiches, and serve.