Heat 1 tablespoon of oil in a large skillet over medium heat. Add shallots; sauté until softened, about 5 minutes. Add garlic, 1/4 teaspoon coarse salt, 1/4 teaspoon thyme, and 1/8 teaspoon allspice. Stir until fragrant, about 30 seconds. Add blueberry pie filling and vinegar. Stir often for about 3 to 4 minutes on low heat. Season with freshly ground black pepper. Remove from heat. DO AHEAD Can be made 2 hours ahead. Let stand at room temperature. Rewarm before using.
Brush grill rack with oil. Prepare barbecue (medium-high heat). Brush salmon on both sides with oil; sprinkle with coarse salt and black pepper.
Grill salmon until just opaque in center, 4 to 5 minutes per side. Transfer to plates. Spoon sauce over salmon and sprinkle with remaining 1 tablespoon mint. Serve immediately with a green veggie of your choice.