Place the water and salt in a large bowl. Stir until salt is dissolved. Add 8 sage leaves, minced garlic and chicken; stir gently. Be sure liquid covers the chicken and allow to stand for 15 minutes.
Transfer chicken to a paper towel-lined plate and pour the liquid over a mesh strainer to reserve the sage leaves and garlic. (No need to reserve the water brine.)
Pat the chicken dry with a paper towel.
Heat a large non-stick or well-seasoned skillet until warm. Add butter and 2 tablespoons oil and heat over medium heat.
Add chicken and cook 5 minutes.
After 5 minutes, add reserved sage and garlic (from the brine).
Turn the chicken and cook another 3 minutes.
Reduce heat to low, cover the pan with a lid and cook 2 minutes.
Test the chicken with a meat thermometer inserted into the thickest part of the breast. Chicken breasts are done when the internal temperature is 160°F.
If needed, replace the lid and cook just until chicken is done.
Remove from the heat (keep lid on) and let rest for 2 minutes.
While the chicken rests, fry the sage leaves: If necessary, add 1 tablespoon more oil to the pan. Heat oil over medium heat. Place the extra 12 sage leaves in the hot oil and cook for 3-5 seconds per side or until crispy. Turn off heat and transfer leaves to a paper towel to dry.
To serve the chicken:
Place chicken breasts on a serving dish and drizzle with the pan juices. Top with crispy sage leaves.
