Preheat oven to 375ºF, place a rack in the center of the oven.
Season the chicken with salt, pepper and thyme. Arrange bacon on a cutting board overlapping the long edge of every 3 slices.
In a small bowl, combine the onion, eggs, parsley and blue cheese. Stuff each chicken breast with the mixture, roll into bundle and secure with butcher twine.
Place a bundle of chicken on the three overlapping slices of bacon and wrap them to cover the chicken, like the stripes on a candy cane or barber poll. Spray wrapped chicken with cooking spray and cook on a slotted pan to deeply golden and crispy, 35-40 minutes. Cool to handle.
Place a bed of greens on a plate and slice the rolls, arrange on top.