Combine 10 cups water, 1/2 cup kosher salt, brown sugar, mustard seeds, peppercorns, thyme and onions in a large glass bowl or a plastic container. Add the pork, cover and refrigerate for at least 4 hours and up to 12 hours. Thirty minutes before grilling, remove the pork from the brine, rinse with cold water, pat dry and let sit out at room temperature.
Prepare a charcoal grill for direct and indirect cooking.
Combine the paprika, cumin, mustard, fennel, the remaining 4 teaspoons salt and ground pepper in a bowl. Rub the pork with the spices and drizzle with canola oil. Sear the pork over direct heat on both sides until lightly golden brown and a crust has formed, about 5 minutes per side. Move the pork over indirect heat (inside of grill should be at about 375 degrees F) and cook, brushing with the Sherry Vinegar BBQ Sauce every 5 minutes or so, until a thermometer inserted in the center registers 145 degrees F, about 1 hour and 15 minutes. Brush with the sauce every 10 minutes or so after the first 45 minutes.
Remove from the grill, loosely tent with foil and let rest 15 minutes before slicing. You can either slice into individual chops, or slice the loin off the bones and thinly slice.
Combine the ketchup, vinegar, chicken stock, brown sugar, mustard, paprika and thyme in a medium saucepan and simmer over medium heat until reduced by half. Season with salt, pepper and honey. Let cool to room temperature.
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