In a medium saucepan over medium heat, combine fresh or frozen blueberries, sugar, lemon juice, balsamic vinegar, and thyme. Stir until it bubbles, then reduce heat to low and let it simmer for about 15 minutes, or until thickened. Remove from heat and cool before refrigerating.

In a food processor, add mayonnaise, fresh basil leaves, garlic, olive oil, and lemon juice. Blend until smooth and creamy. Transfer to a bowl, cover, and chill in the refrigerator.

Season the burger patties with salt, pepper, garlic salt, and onion powder. Preheat grill over medium-high heat. Cook patties for 5-7 minutes per side until desired doneness, adding Havarti cheese during the last minute to melt.

Assemble the burgers starting with toasted brioche buns. Layer arugula on the bottom, followed by the cooked patty with melted cheese, blueberry sauce, and crispy bacon. Spread Basil Garlic Aioli on the top bun, close the burger, and serve.