Cut chicken into smaller pieces, filleting if necessary to create equal thickness pieces.
Heat large skillet to medium-high, melt butter. Brown chicken in sizzling butter, both sides, then set aside in casserole dish.
Add more butter to skillet if necessary and sauté mushrooms, olives, pesto, garlic, and salt & pepper.
Add chicken broth (or wine) and “glaze” the pan, collecting all the bits of chicken and butter from the sides.
Add the olives, sour cream and milk and stir constantly over medium heat until it comes to a slight boil. Reduce by half.
Transfer to casserole dish, ensure chicken pieces are covered, sprinkle feta over top, cover, and bake at 325°F for 20-30 minutes.