Season pork with salt and black pepper. Heat oil in a large skillet over high heat. Add pork; sear on all sides until browned, about 3 minutes per side. Transfer to a slow cooker.

Add shallots and celery to same skillet over medium heat; cook and stir until begin to soften, 3 to 4 minutes. Pour in apple cider vinegar; cook, scraping up any browned bits, until liquid nearly evaporated, 4 to 5 minutes. Add to slow cooker.

Add apple cider, garlic cloves, and bay leaf to slow cooker; cover. Cook on Low until fork-tender but not falling apart, about 6 hours, turning pork every 1 to 2 hours. Transfer pork to a plate; cover loosely with foil.

Strain cooking liquid through a fine-mesh-sieve, discarding solids, into a large saucepan over high heat. Bring sauce to a boil, then decrease heat and cook, skimming fat from top, until reduced to 1/4 of original volume, about 10 minutes.

Off heat, stir Dijon mustard and cayenne pepper into sauce; slowly whisk in cold butter until incorporated. Sprinkle in fresh herbs; season with salt and black pepper.

Cut pork into 1/4-inch thick slices. Serve with sauce.