Pulled BBQ Chicken Sandwiches

from Mom

2 lbs boneless chicken breasts
1 1/2 to 2 cups BBQ sauce
1 ½ cups shredded Monterey Jack Cheese
4-6 cloves garlic, minced or crushed
1/2 cup apple cider vinegar
1 onion, finely chopped
6 ciabatta rolls

Season chicken with salt and pepper and place in a heavy pot with the onion, garlic and just enough water to cover (about 1 to 1 1/2 cups). Add the BBQ sauce and vinegar and bring to a boil. Reduce the heat and simmer until chicken is cooked through (about 15 minutes) Remove the chicken and shred with forks. Boil the sauce until reduced by half (about 15 minutes). Add the shredded chicken and heat through. Spoon the mixture onto the rolls and top with the cheese.