Preheat oven to 450F and prepare a baking sheet with a wire rack on top. (You can also bake directly on the baking sheet.)
Heat a large skillet over medium-high heat with the olive oil. Add the diced onion and cook for 5-6 minutes until they begin to soften and slightly brown. Add the garlic and cook for another 30-60 seconds until fragrant.
Add the green chiles and soup to the skillet, stirring to fully incorporate. Remove from the heat and add the shredded cheese, stirring until melted and evenly distributed. Add the shredded chicken, stir together, and set aside.
Wrap the tortillas in a damp paper towel and microwave for 60 seconds. Place 4 tortillas at a time (to keep them warm) on the wire rack. Fill one half of each tortilla with the chicken mixture and fold over to seal. Repeat to fill all the tortillas as evenly as possible.
Spray the tops of the tacos with a tiny bit of cooking spray and bake for 25-30 minutes until the tacos are as crispy as you'd like. Different sizes of baking sheets will affect bake time so keep an eye on the tacos. Optional: place a second baking sheet on top of the tacos for the first 10 minutes to prevent any tacos from opening during baking.