Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with aluminum foil and grease with avocado oil.
Pound chicken thighs using a meat mallet until they are uniform and fairly thin. Place a slice of Cheddar-Monterery Jack cheese and 2 asparagus spears in the center of each thigh. Roll thigh around the cheese and asparagus; wrap each with 1 bacon slice.
Arrange chicken rolls on the prepared baking sheet; season with salt and pepper.
Bake in the preheated oven until bacon is crisp, asparagus is slightly wilted, and chicken is no longer pink in the center, about 35 minutes. An instant-read thermometer inserted into the chicken should read at least 165 degrees F (74 degrees C).