Prep the chicken. If the breasts are very thick, slice them horizontally to create thinner cutlets (or pound them to even thickness). Pat dry with paper towels and season generously with salt and pepper on both sides. Wet chicken = sad, non-browned chicken, so don't skip the drying step!
Get that golden sear. Heat olive oil in a large skillet over medium-high heat until shimmering. Add chicken and cook for 4-5 minutes per side until golden brown and almost cooked through (it will finish cooking in the sauce). Transfer to a plate and cover loosely with foil. Look at that beautiful color you just created!
Build your flavor base. In the same pan (don't you dare wash it - those brown bits are flavor gold!), reduce heat to medium and add butter. Once melted, add minced garlic and shallot, cooking for 1-2 minutes until fragrant and softened but not browned. Burnt garlic is bitter garlic, and we're going for delicious here.
Create the roux. Sprinkle flour over the garlic and shallots, stirring constantly for about 1 minute to cook out the raw flour taste. This will help thicken our sauce without lumps.
Make it saucy. Slowly pour in chicken broth while whisking continuously to prevent lumps. Bring to a simmer and let it reduce for 2-3 minutes, scraping up all those delicious browned bits from the bottom of the pan.
Bring on the cream. Pour in the heavy cream and add thyme, rosemary, half the parsley, and red pepper flakes if using. Stir to combine and let simmer for 2-3 minutes until it starts to thicken slightly.
Cheese, please! Stir in the Parmesan cheese until melted and smooth. Add lemon juice to brighten all the flavors. Taste and adjust seasonings – need more salt? Pepper? Add it now.
Reunite the chicken with its sauce. Return the chicken and any accumulated juices to the pan, nestling it into the sauce. Reduce heat to low, cover, and simmer for 5-7 minutes until chicken is completely cooked through (internal temperature of 165°F/74°C).
Finish with flair. Sprinkle with remaining fresh parsley and serve directly from the skillet for a rustic presentation, or transfer to plates. Spoon plenty of that liquid gold sauce over each piece of chicken!