In a medium bowl, mix together brown sugar, salt, cayenne pepper, 4 cloves garlic, thyme, and rosemary. Place pork in a roasting pan and rub sugar mixture all over pork. Cover and transfer to refrigerator; let marinate for 2 hours.
Remove pork from refrigerator and let come to room temperature. Preheat oven to 400 degrees.
Brush rub off of pork; transfer to oven and roast for 45 minutes. Decrease temperature to 250 degrees. Cook until meat is very tender and shreds easily, about 8 hours. Immediately shred meat with a fork and transfer to a large bowl.
In a large saucepan, heat olive oil over medium-high heat. Add remaining 2 cloves garlic, shallots, and chiles; cook stirring, until fragrant and softened, about 3 minutes. Add clams and wine; cover and cook until clams open, 5 to 8 minutes.
Pour clams over pork; drizzle with olive oil and sprinkle with parsley. Serve immediately.
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