Preheat the oven to a low broil. Butter the bread and place on a baking sheet. Broil until golden, 2 to 3 minutes, and remove from the oven.
Spread Miss Dixie's Remoulade on both sides of the bread. Layer on the turkey, tomatoes, pepperoncini and romaine. Top with other half of bread and serve immediately.
In a food processor, add all ingredients and process until smooth, 25 to 35 seconds depending on blender speed. Scrape down sides as needed. Refrigerate until ready to use.
Combine all the ingredients together in a large re-sealable plastic bag. Place in a bowl, to catch any leaks, and refrigerate 12 to 24 hours.
Preheat the oven to 325 degrees F.
Remove the turkey breast from the brine, drain well and pat dry with paper towels.
Place the turkey breast, skin-side up, on a baking sheet fitted with a wire rack. Place in the oven and cook for 1 hour 15 minutes. Turn the oven up to 400 degrees F and cook for an additional 10 to 15 minutes, or until the internal temperature is 160 degrees F and the skin is nicely browned. Remove from the oven, cover with aluminum foil and let rest for 10 minutes.
Meanwhile, preheat the grill to medium heat and oil the grates generously with vegetable oil.
Once the turkey has rested, cut the meat off the bone and carve into 3/8-inch thick slices. Place the slices on the grill and cook 1 to 2 minutes on each side, just until grill marks develop. Remove from the grill.