Preheat the grill to medium heat (the grill should maintain a constant temperature of 350 degrees F). Place a drip pan filled half-way with the chicken stock on the briquettes. Season the pork butt with salt and pepper and place on the grates of the grill over the drip pan. Close the cover of the grill and let the pork cook for 1 hour. Turn the pork over and continue grilling for 2 to 3 hours, or until it reaches an internal temperature of 160 degrees F. More chicken stock may be needed to refill the drip pan during grilling. Remove the pork from the grill and let rest for 15 minutes. When it is cool enough to handle, shred the pork into strands with your fingers. Add the shredded pork to the BBQ Sauce and serve on sandwich buns with the Pickled Jalapenos.
Heat oil in a medium saucepan on the grates of the grill. Add the onion and jalapeno and cook until soft. Add the fresh tomatoes, canned tomatoes and juices, vinegar, honey, brown sugar and Worcestershire sauce, and cook until the sugar has completely melted and the sauce is slightly reduced and thickened. Season with salt, to taste. Add the shredded pork and stir to coat.
Combine the vinegar, sugar, peppercorns, seeds, and salt in a medium saucepan and bring to a boil. Let boil for 2 minutes, and then remove from the heat and let sit until cooled to room temperature.
Place the jalapenos, stem side up, into the jar and pour enough cooled vinegar mixture over them to cover. Pack the cilantro sprigs into the jar. Cover and refrigerate for at least 24 hours and up to 4 days.