Preheat the oven to 425°F.
Butterfly the chicken breasts by slicing them lengthwise three-quarters of the way through, keeping the knife level and avoiding cutting all the way to the other side.
Combine the cream cheese, parmesan, garlic, onion, salt, thyme, and lemon juice in a small bowl to create the cheese filling.
Fill each butterflied breast with half of the cheese mixture, leaving a half-inch margin at the edges, and sprinkle with fresh parsley.
Line a baking sheet or casserole dish with parchment paper or coat it with cooking spray, then place the stuffed chicken breasts on the prepared surface.
Mix the melted butter and lemon zest together and brush the mixture over the tops of the chicken breasts.
Bake at 425°F for 30 minutes, basting the tops after 20 minutes to promote browning, until the internal temperature reaches at least 165°F in the thickest part.
Allow the chicken to rest for 5 minutes, then slice each breast in half crosswise and serve with your preferred side dishes.