Slice chicken breasts in half horizontally to create thin cutlets, or pound to an even thickness with a meat mallet. Season both sides generously with salt, black pepper, and a small pinch of Italian seasoning.

Heat olive oil in a large skillet over medium heat until shimmering. Add the chicken and sear for 4 to 5 minutes per side without moving, until a deep golden crust forms and the internal temperature reaches 165 degrees F. Remove from skillet and set aside. Leave drippings in the pan.

Reduce heat to medium-low. Add the butter to the same skillet and let it melt. Add the minced garlic and cook for about 60 seconds, stirring constantly, until fragrant. Watch closely as garlic burns quickly.

Pour in the heavy cream and stir to scrape up all the browned bits from the bottom of the pan. Stir in the freshly grated parmesan and remaining Italian seasoning. Simmer for 3 to 5 minutes, stirring often, until the sauce thickens and coats the back of a spoon.

Return the chicken to the skillet and spoon the sauce over each piece. Simmer for 2 to 3 more minutes to warm through and let flavors finish coming together. Garnish with fresh parsley and serve immediately.