Generously season the chicken with salt and pepper on both sides. Heat vegetable oil in a large skillet. Cook chicken breasts on medium-high heat - about 2 minutes on each side, to brown a bit. Chicken doesn't have to be cooked through - you'll continue cooking it later. Remove the chicken from the skillet.
Add minced garlic to the same skillet - cook on medium heat for about 30 seconds, scraping the bottom of the pan. Deglaze the pan with the small amount of chicken stock. Add the remaining chicken stock (total of 1 cup).
Add half the bacon (cooked, fat should be drained off, and chopped into small chunks) to the chicken broth.
Add the chicken back to the pan, on top of bacon and in the chicken broth. Arrange 5 thin lemon slices around chicken breasts - and cook, simmering on low heat, covered, for about 20 minutes, until the chicken is completely cooked through, and is no longer pink in the center.
After the chicken is completely cooked, remove it from the skillet. Remove lemon slices from the skillet - it's very important that you remove them now, do not leave them in for the sauce otherwise it will be too sour. Add 1 cup half and half to the skillet. Bring to boil and mix everything well, scraping from the bottom. Add 1/2 cup shredded Asiago cheese and stir to melt completely, about 30 seconds. Immediately reduce to simmer, add chicken breasts back to the skillet and reheat.
To serve, spoon some of the sauce over the chicken breasts, and sprinkle with the remaining chopped bacon and chopped parsley.