Place an oven rack 6 inches from broiler. Heat broiler to high. Line a rimmed baking sheet with foil; spray foil lightly with cooking spray.*
In a large bowl, stir together ground turkey, 1 ounce blue cheese, red onion, tarragon and hot sauce until well combined. Form mixture into 4 round, 3/4-inch thick patties. Place patties on prepared baking sheet.
Broil patties 10 minutes, flipping once, until browned and a meat thermometer inserted in center of patties reads 165 degrees F.
Meanwhile, in a small bowl, stir mustard and honey until combined. Spread honey mustard on burger buns, then top with mayonnaise, lettuce, red onion and/or any other desired toppings. Top each burger with a patty, then top each patty with remaining blue cheese crumbles and tarragon leaves.
*NOTE: Alternatively, patties can be grilled. Heat a gas or charcoal grill to medium heat and cook patties on greased grates (grill covered), flipping once, 10 minutes until a meat thermometer inserted in center of patties reads 165 degrees F.