Preheat oven to 325F.
Pat pork dry then season with salt, pepper and fennel. Heat just enough olive oil to coat the bottom of a Dutch oven over medium to medium-high heat. When oil smokes, add meat and caramelize on all sides; remove to a plate.
Add garlic cloves, onion, celery and herb bundle to pan, and season with salt and pepper. Cook to soften a bit, 5 minutes. Deglaze the pan with vermouth or wine then add lemon slices, stock and pork back to the pot. Cover and roast 3 hours.
Bring a large pot of water to boil for pasta.
Remove the pork to a platter, strain sauce over pot. Cook and reduce by half then add lemon juice and honey.
Cook pasta in salted water to al dente.Add a ladle of starchy water to sauce just before straining.
Pull pork, separate out fat.
Toss the pasta with sauce, pork and wilt in the arugula. Add some shaved Parm and serve on a warm platter or in shallow bowls.