Season chicken thighs with salt and pepper.
Sear chicken in a pan with 2/3 of the olive oil and 1/2 of butter until browned on all sides.
Add smashed garlic, fresh sage leaves, and lemon zest to the pan. Stir.
Pour in milk (enough to almost cover the chicken)
Add the dried wild mushrooms.
Simmer gently until the chicken is cooked.
Remove chicken and shred when cooled.
Strain and reserve the milk, discarding the garlic, sage, and lemon zest.