For the Court Bouillon: In a stock pot over medium-high heat, combine all ingredients and 3 kilograms water. Bring to a simmer, then reduce heat and cook 45 minutes. Season with salt, then transfer to an airtight container and refrigerate overnight.
For the Sweetbreads: Place sweetbreads in a nonreactive container and cover with water. Refrigerate overnight. The next day, warm Court Bouillon in a large stock pot over medium-low heat. Using a slotted spoon, remove sweetbreads from water and add to the pot. Bring mixture to a simmer, then reduce heat and cook until the internal temperature of the sweetbread reaches 125°F. Remove sweetbreads and transfer to a paper-towel lined plate. Place a second plate on top of sweetbread and press lightly. Refrigerate. Once cooled, clean and portion sweetbreads into 2-ounce pieces. Set aside.
For the Piperade: In a large sauté pan over medium flame, heat oil. Add alliums and sauté until lightly caramelized. Add bell peppers and chiles. Cook until tender, then add anchovies and tomato paste. Cook 3 minutes. Deglaze pan with wine and fish sauce, then continue to cook until liquid has nearly evaporated and a jam-like consistency is achieved. Transfer mixture to a Vitamix blender. Add garlic and purée until smooth. Season with salt, vinegar, and Calabrian chile. The piperade should be spicy. Transfer to an airtight container and refrigerate.
For the Pimenton Oil: In a Vitamix blender, blend all ingredients on high speed until the oil begins to steam. Strain, transfer oil to a squeeze bottle, and reserve.
For the Citrus Salt: In an airtight container, combine all ingredients. Reserve.
To Assemble and Serve: Remove Piperade from the refrigerator and let it come to room temperature. In a large rondeau over high flame, heat 2 inches of oil to 350°F. Season two 2-ounce portions of Sweetbreads generously with salt and pepper. Add to oil and fry 3 minutes, or until golden and crispy. Transfer to a paper towel-lined plate and let drain. In a mixing bowl, add 2 tablespoons Pimenton Oil. Season with lime juice and whisk until emulsified. Set aside. Skewer fried Sweetbreads and transfer to a serving plate. Spoon seasoned Pimenton Oil over top followed by a dollop of Piperade. Garnish with a sprinkle of Citrus Salt, Espelette pepper, and mint.
