1. Slice the chicken breasts horizontally (similar to a butterfly cut) all the way through to create two thinner pieces. To do this, place your hand flat on top of the chicken breast to keep it steady, and use a sharp knife to carefully cut through the middle from one side to the other. Place the chicken pieces side by side on a cutting board and cover with plastic wrap. Gently pound with the smooth side of a meat mallet until even thickness. Season both sides of the chicken with salt and pepper.
2. Place the flour on a large plate. Working with one at a time, coat both sides of each piece of chicken in the flour.
3. In a large skillet, heat the avocado oil over medium-high heat. Add the chicken pieces (in one layer) and cook, undisturbed, until golden brown, about 3 mins per side. Remove the skillet from the heat and transfer the chicken to a large plate.
4. Return the skillet to the stove over medium-heat and add the butter and chopped broccoli. Cook for 1-2 mins until the broccoli is bright green and starting to become tender, then add the finely chopped garlic and cook for 1 more min. Add the chicken broth, cream cheese, 1/4 teaspoon kosher salt, and 1/4 teaspoon pepper. Cook while stirring until the cream cheese melts, then add the milk. Bring to a simmer and cook, stirring occasionally, until it reduces by half, 3 to 4 minutes. Taste and adjust seasoning if desired.
5. Return the chicken to the pan, nestling it in the sauce. Continue cooking until the sauce thickens up a bit and the chicken gets heated back through, 1-2 minutes.
6. Serve with chopped fresh parsley on top and enjoy!
