Pat the chicken breasts dry with paper towels. Season both sides evenly with kosher salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the skillet and cook for 5 to 6 minutes on one side without moving them, until golden brown.
Flip the chicken breasts and cook for another 5 minutes, until the internal temperature reaches 165°F (74°C). Remove the chicken from the skillet and set aside on a plate.
Reduce the heat to medium. Add the minced garlic to the skillet and sauté for 30 seconds until fragrant, stirring constantly to prevent burning.
Pour in the chicken broth, lemon juice, and add the lemon zest, thyme, and rosemary. Stir to combine and bring the sauce to a simmer.
Cook the sauce for 3 to 4 minutes until it slightly reduces and thickens.
Turn off the heat and stir in the unsalted butter until melted and the sauce is glossy.
Return the chicken breasts to the skillet and spoon the sauce over them to coat.
Sprinkle the chopped fresh parsley over the chicken and sauce before serving.