Place the 3 boneless skinless chicken breasts in the bottom of a 6‑quart slow cooker; sprinkle with 1 tablespoon minced garlic and 1½ teaspoons Italian seasoning, then pour the 24‑oz jar of spaghetti sauce over the chicken.
Cover and cook on LOW for 6–8 hours, until the chicken is tender and easily shredded; then shred the chicken with two forks and stir to combine with the sauce.
Preheat the oven broiler. Slice the slider rolls in half and arrange the cut sides up on a rimmed baking sheet; broil briefly until golden brown, watching carefully to avoid burning.
Preheat the oven to 350°F (175°C). Place the bottom halves of the buns in a 9×13‑inch baking dish or on a rimmed baking sheet.
Top the bottom buns with a layer of shredded mozzarella, add a generous portion of the shredded chicken with sauce, then sprinkle more mozzarella over the chicken and place the top buns on each sandwich.
In a small saucepan over medium heat, melt the ½ cup butter with 1 teaspoon garlic powder and 1 teaspoon Italian seasoning; remove from heat and stir in 1/3 cup grated Parmesan.
Brush the butter‑Parmesan mixture over the tops of the buns, then bake in the preheated 350°F oven until the buns are toasty and the cheese is melted, about 10–15 minutes.
Serve the sliders hot, spooning any extra marinara sauce over the sandwiches as desired.