Preheat oven to 275F.
In a small saucepan, combine the Balsamic Vinegar and brown sugar, bring to a boil, reduce heat to low and simmer until sugar has dissolved and reduction has thickened. Set balsamic reduction aside until ready to use.
Brush a baking dish or baking pan (a little larger than length and width of salmon) with 2 teaspoons extra virgin olive oil and place the salmon, skin side down, in the dish. Place the tomatoes, still attached to the vine, on each side of the salmon. Sprinkle the salmon and tomatoes with salt, pepper, favorite herb seasoning, 2 tablespoons brown sugar and the chopped basil. With a sharp knife, make three cuts (½“ deep) along the length of the salmon. One down the middle and one down the middle of each half. The cuts should NOT go all the way through the salmon.
Drizzle the salmon with olive oil then stuff the tomato and mozzarella slices into the cuts of the salmon, alternating between the tomato and mozzarella slices as you go down the salmon.
Drizzle the salmon with the balsamic-sugar mixture.
Bake the salmon at 275F for 30 minutes or until tender when a fork is inserted in the thickest part (or when a meat thermometer registers 115F in the thickest part). The salmon may look a little underdone – this happens when baked slowly.
Leave the salmon in the oven and turn the temperature to BROIL.
Broil 2-3 minutes, or until the salmon begins to get a little color. Watch closely.
Check the temperature of the salmon with a meat thermometer. The finished salmon should register 120F-125F.
Remove the salmon from the oven and sprinkle with fresh basil leaves.