Preheat the oven to 400°F (200°C) and lightly grease a casserole dish.
Heat a skillet over medium-high heat and add the olive oil.
Add the minced garlic to the skillet and cook until fragrant, about 1 minute.
Add the shredded chicken to the skillet and cook just until warmed through, then remove from heat and set aside.
In a mixing bowl, combine the sour cream, salsa verde, and half of the chopped cilantro; season with salt and pepper.
Toss the warmed shredded chicken with about half of the salsa verde mixture to make the filling.
Divide the filling among the tortillas, roll each tortilla up, and place seam-side down in the prepared casserole dish.
Pour or spread the remaining salsa verde sauce over the rolled enchiladas and sprinkle evenly with the shredded cheese.
Cover the casserole with aluminum foil and bake for 15 minutes. Remove the foil and bake an additional 10 minutes until the cheese is melted and lightly golden.
Remove from the oven and garnish with the remaining chopped cilantro and the chopped red onion before serving.