Sauce: In a small saucepan, bring wine to a boil and reduce by half. Place sugar in a heavy saucepan and cook over medium heat without stirring. When sugar begins to caramelize and turn brown (about 7 minutes), stir with a wooden spoon until all the sugar is dissolved and medium-golden brown. Off heat, slowly pour vinegar into the caramelized sugar. (The sugar will seize, but just keep stirring and the two ingredients will combine.)
Stir in the reduced wine and blueberries. Return to the heat and whisk until well blended. Simmer, stirring occasionally, until reduced to a consistency that coats a spoon (the consistency of maple syrup), about 15 minutes. Add lime juice and adjust flavor with the salt and pepper. Stir in butter. Keep warm to serve with pork.
Rice: Heat a medium saucepan with butter; add leeks, celery and carrots and sauté until vegetables soften and are translucent. Add wild rice and stock, season with salt and pepper and simmer 10–15 minutes, until the stock is absorbed. Keep warm.
Preheat oven to 350°.
Season pork with salt and pepper. Heat a sauté pan over medium heat with butter and olive oil. Add pork and cook on all sides until nicely browned. Place in the oven for 15–20 minutes, until the meat is 145° when tested with a meat thermometer. (The size of the meat will affect the cooking time, so check early.) Let rest 10 minutes before slicing into thin pieces.
Serve a scoop of wild rice topped with pork slices and drizzle with blueberry gastrique.