In a small bowl, whisk together mayonnaise, apple cider vinegar, dried dill and paprika and set aside.
Season chuck roast with salt and pepper on all sides, then sprinkle with flour making sure the entire roast is coated.
In a large skillet, heat vegetable oil to almost smoking and sear roast on both sides. Transfer to slow cooker.
Add mayonnaise mixture, pepperoncini and butter to slow cooker and cook on low for about 8 hours, until roast is fork tender. Shred meat and serve.