Set the four fillets on a cutting board and evenly zest one of the limes over the fillets. Season well with vanilla salt (or sea salt). Turn the fillets and repeat the seasoning process using the second lime and more salt.
Cut 4 separate tablespoons of the unsalted butter and, using your fingers, flatten them to better match the size of the halibut fillets. Place each fillet into a vacuum-sealing bag, then place one flattened piece of the butter against the skinned side of each fillet. Vacuum seal each bag, and place them in the refrigerator for 30 minutes to allow the lime and salt to permeate the flesh. During this time, using the sous vide wand, bring the water temperature to 125°F. (See notes if you don’t have a sous vide wand.)
After 30 minutes, place the halibut fillets into the sous vide bath for 45 minutes (at 125°F). While they cook, juice the limes and measure 1/4 cup of strained lime juice. Reserve any remaining lime juice for another purpose. Place the quarter cup of lime juice in a small saucepan and add the dessert wine and brown sugar; bring to a low boil. Cook the mixture until the liquid has reduced to around 2 tablespoons (it can be more, but not less). Remove from the heat and set aside.
As you near the end of the cooking time, reheat the juice/wine mixture over medium-low heat. Whisk in 1 tablespoon of the remaining butter at a time until smooth and creamy. After the 5th tablespoon of butter, add the vanilla and whisk well. Whisk in the final tablespoon of butter, then remove from the heat and set aside covered, to keep warm.
When the fish is done, heat a skillet to medium-high, then carefully transfer each fillet from its bag, skinned side up, into the skillet. The residual butter should help it brown nicely. Transfer to 4 plates, browned side up and nap the sauce over and around the fish. If desired, garnish with mint leaves.