Heat a large skillet over medium-high heat. Add the olive oil and allow it to heat for a minute.
Add the diced onion and minced garlic to the skillet. Sauté for about 2-3 minutes, or until the onions become translucent and fragrant.
Add the ground turkey to the skillet. Use a spatula or wooden spoon to break it apart as it cooks. Season with salt and pepper to taste. Cook the turkey, stirring occasionally, until it's browned and fully cooked, usually about 5-7 minutes.
In a separate bowl, mix together the ketchup, sugar-free BBQ sauce, Worcestershire sauce, vinegar, and yellow mustard. Stir until well combined.
Pour the sauce mixture over the cooked turkey in the skillet. Stir to coat the turkey evenly with the sauce. Reduce the heat to low and let it simmer for about 5 minutes, allowing the flavors to meld together.
While the mixture is simmering, lightly toast the hamburger buns in a toaster or oven.
Once the turkey mixture is heated through and the sauce has thickened slightly, remove the skillet from the heat.
To assemble the turkey sloppy joes, place a scoop of the turkey mixture onto the bottom half of each toasted bun.
Sprinkle a generous portion of shredded pepper jack cheese over the turkey mixture.
Top each sandwich with the other half of the bun.
Serve your delicious turkey sloppy joes hot and enjoy!