Brine chicken in 3/4 cup Kosher salt, sugar, and water. Refrigerate chicken in brine for 1 hour; pat chicken dry and store overnight, uncovered in fridge. Add carrot juice to saucepan and reduce to thick consistency on high heat, 10–15 minutes. Whisk vigorously if juice separates. Whisk in butter; set aside to cool. In pot, cover wild rice with chicken stock. Bring to simmer and cook 45 minutes. Season with Kosher salt as desired. Preheat oven to 400 degrees. In a frying pan on medium-high heat, sweat onions in olive oil until soft. Add curry spice and toast until aromatic. Add vinegar and salt; stir well. Fold through sun-dried tomatoes. Place chicken skin-side up on roasting pan fitted with rack. Brush chicken with canola or olive oil and season as desired. Roast about 25–35 minutes or until golden brown; internal temperature should be 165 degrees. Drizzle with roasting juices; add salt and chopped parsley before plating. To plate, add carrot butter to wild rice; scoop 1/2 cup rice onto each dish. Place chicken skin-side up on top of rice. Dollop with onion, curry, and tomato mixture.