Preheat the oven to 400 degrees F and spray a 24-cup mini muffin tin with nonstick cooking spray.
Delicately press the wonton skins into the mini muffin tin, being sure to make the base of the wonton skin is flat (this will ensure that the taco cup will stand flat when you remove them from the pan). Spray the wontons lightly with nonstick cooking spray and transfer them to the oven to bake until they are golden brown and crisp, 7 to 10 minutes.
In the meantime, heat a nonstick pan over medium-high heat. Add the olive oil and swirl to coat the pan. Add in the onion and sauté until translucent, about 4 minutes. Add in the garlic and stir to combine. Add in the turkey, breaking up with a wooden spoon. Next add in the chili powder, cumin, dried oregano, smoked paprika, and salt. Cook, stirring frequently, until the turkey is cooked through, about 5 to 7 minutes.
To assemble, keep the taco cups in the mini muffin tin (this will help with any unstable taco cups). Add a little cheese to each of the taco cups, then top them with the ground turkey mixture. Next add your desired toppings such as shredded lettuce, diced avocado, salsa, sour cream, pickled jalapeños, and chopped cilantro.