In the bottom of a slow cooker, add sliced onion, apple cider, molasses, apple cider vinegar, smoked paprika, garlic powder, cumin, salt, and black pepper. Stir to combine.
Add chicken breasts to slow cooker. Cook on low for approximately 6 to 8 hours, until cooked through. You can also use a pressure cooker and cook for 15 to 20 minutes.
Remove chicken from the slow cooker or pressure cooker to a large bowl. Using two forks, shred chicken. Set aside.
In a medium bowl. toss together ingredients for the apple cabbage slaw until well combined.
To assemble the sliders. add a good helping of shredded chicken to the bottom halves of the toasted pretzel slider buns. Add a slice of white cheddar cheese on top of each.
Place bottom halves of the sliders on a sheet pan. Place under the broiler set to high and broil until the cheese is melted, approximately 2 minutes.
Remove from heat and top with your favorite BBQ sauce, if desired. Add a good pinch of the apple cabbage slaw on top. Finish with the top half of the slider bun. Repeat with remaining sliders and serve.