Warm water in a large pot over high heat. Add salt and stir to dissolve. Stir in brown sugar, orange, lemon, lime, cilantro, garlic, rosemary, thyme, bay leaves, peppercorns, fennel, coriander, and cloves. Bring to a boil, reduce heat to low, and cover. Let brine simmer for 20 minutes.
Fill a sink with ice water. Remove brine from heat and place pot into the sink. Cool, stirring, until brine reaches room temperature. Pour into a large plastic or glass vessel such as a 12-quart Cambro(R). Add pork tenderloin pieces. Cover and let soak 6 hours to overnight.
Remove loins from brine and rinse. Let rest at room temperature for 30 to 45 minutes while you prep the grill. Preheat the grill for indirect heat at 275 degrees F (135 degrees C).
Place loins on cooler side of the grill and cook, rotating every 20 to 30 minutes, until an instant-read thermometer inserted into the centers read 130 to 135 degrees F (54 to 57 degrees C), 35 to 40 minutes.
Paint loins with vegetable oil and move over the direct heat side of the grill. Sear until golden brown all over and internal temperature just reaches 145 degrees F (63 degrees C), about 2 minutes per side.
Remove loins from heat, place on a serving dish, and tent with foil. Let rest for about 5 minutes. Slice into 1/2- to 1-inch-thick medallions.
