Place chicken into the crockpot. In a medium bowl, mix together marinara, broth, basil, garlic and ½ teaspoon salt. Pour over chicken and stir to coat. Cook on low 5-6 hours. Remove chicken from crockpot, shred, and return to crockpot; stirring the chicken to coat in the sauce.
Heat oven to 350 degrees. Mix together melted butter, garlic, and parsley. Slice rolls in half and place on foil-lined cookie sheets. Brush each roll half with butter mixture. Toast in over for 3-4 minutes to lightly toast. Remove from oven and portion chicken on one half of each sandwich. Top with 2 slices of cheese and the other half of the sliced roll. Cut in half and serve.