Mix together the softened butter, chopped parsley, and crushed garlic in a small bowl. Form the butter into two small cylinders and wrap them in cling wrap. Put these wrapped butter logs in the freezer to harden for about 10 -15 minutes.
Meanwhile, put the chicken breasts between two sheets of cling film (plastic wrap) on the counter top and pound them until they are flat and about ¼ inch (0.6 cm) in thickness.
Season the chicken on both sides, with salt and pepper.
Take the butter from the freezer, unwrap it, and discard the cling film (plastic wrap). Place a butter log in the center of each flattened chicken breast.
Wrap the chicken breast around the butter, so that the butter is concealed in the center and all ends are tucked in.
Wrap the chicken breast rolls in cling film (plastic wrap) to secure the cylindrical shape and twist the ends to hold. Put the chicken rolls into the freezer for 30 minutes to allow the chicken to firm so that it will retain its cylindrical shape.
Unwrap the chicken and discard the cling film (plastic wrap). Put the frozen breast rolls into a food-grade cooking pouch and vacuum seal the pouch. Submerge the pouch in the water bath and leave to cook for at least 2 hours.
Once the chicken has cooked, remove the rolls from the pouch and carefully pat them dry with paper towels.
Put the flour, beaten egg, and breadcrumbs on three separate plates.
Heat the oil in a heavy bottomed saucepan over a high heat.
Dredge the chicken rolls in the flour, then the beaten egg, and finally the breadcrumbs, so that they are fully covered in crumbs. Once the oil reaches 375°F (190°C), carefully put the rolls into the oil and fry on both sides until golden. It should take less than a minute.
Place the rolls on some kitchen paper (paper towels) to drain off excess oil; serve straight away.