In a bowl, add ground turkey, chorizo, garlic, onion, Worcestershire sauce, paprika, cumin, oregano, salt, and pepper. Mix until well combined. Place in the fridge for 10 minutes. You can also do this the day before.
Preheat oven to 450 degrees F. In a bowl, toss together shoestring potatoes, paprika, salt and pepper. Transfer shoestring potatoes to a lined baking sheet. Bake for 15-20 minutes or until golden brown. Careful not to burn. Set aside.
In the meantime, make the guava BBQ sauce. In a small saucepan, combine the guava paste with the vinegar, rum, tomato paste, lime juice, soy sauce, Worcestershire sauce, garlic and water and bring to a boil. Simmer over low heat, stirring occasionally, until reduced, about 15 minutes. Season the sauce with salt and pepper. Set aside.
Remove chorizo turkey burger mixture from fridge. Form into 4 patties. In a hot skillet, add olive oil. Cook patties, over medium-high heat, until browned about 3 minutes. Reduce heat to medium-low and cook for about 5-6 minutes on each side, until they are all cooked through. Melt a slice of gruyere on top of each patty.
Serve chorizo turkey burgers immediately on toasted hamburger buns with guava BBQ sauce and shoestring potatoes. Enjoy!