Season pork with sea salt and black pepper. Heat oil in a large skillet over high heat. Sear pork on all sides in the hot oil until browned, about 3 minutes per side. Transfer pork to the slow cooker.
Reduce stovetop temperature to medium; cook and stir shallots or onions in the skillet until they begin to soften, 3 to 4 minutes. Pour in 1/4 cup of the apple cider and cook, scraping up any browned bits, until liquid is nearly evaporated, 3 to 4 minutes.
Pour shallot mixture over pork shoulder in the slow cooker. Add Bear Creek apple cider, garlic cloves, rosemary, and bay leaf. Cover, set slow cooker to high, and cook until fork-tender but not falling apart, about 4 hours. Check with meat thermometer to 145 degrees F. Remove pork roast to a plate and cover loosely with foil and let rest 5 minutes.
Pour remaining liquid from the slow cooker through a fine mesh strainer into a large saucepan; place over high heat. Discard bay leaf and other solids. Bring sauce mixture to a boil, decrease heat and cook, skimming fat from the top, until reduced to ½ of the original volume.
Remove sauce from heat and stir in Dijon mustard and cayenne pepper, if desired. Sprinkle in fresh herbs and season with salt and black pepper to taste.
Cut pork into 1/4-thick slices and serve with sauce poured over the top.