Preheat oven to 325 degrees F.
Season the pork shoulder with 2 teaspoons Kosher salt and 1 teaspoon black pepper generously.
In a large 7-8 quart Dutch oven, heat about 3 tablespoons of olive oil over medium-high heat.
Sear the pork shoulder on all sides until browned and a crust formed. Remove from the pot.
In the same Dutch oven, add more oil and cook the sliced onions for 4 minutes over medium heat.
Then, add the garlic and fresh minced thyme and rosemary for another 1 or 2 minutes until fragrant.
Deglaze with white wine, scraping any brown bits with a wooden spoon.
Then, add chicken broth, apple cider, honey mustard, apple cider vinegar, minced thyme and rosemary, and the bay leaves.
Season with salt and pepper to taste. Stir to combine and bring to a simmer.
Then add the seared pork back into the pot, and arrange the whole sprigs of thyme and rosemary around it.
Bring back to a low simmer. Then, cover with the lid tightly and braise in the preheated oven for 2.5 to 3 hours until tender.
Remove the Dutch oven from the oven and add the sliced apples, gently pushing them under the braising liquid.
Return to the oven for another 30 to 45 minutes until fall-apart tender and the apples are softened.
Shred the meat and discard the bones. Serve with mashed potatoes or your favorite sides.
