Prep and dredge the chicken: Pat chicken cutlets thoroughly dry with paper towels. Season both sides evenly with kosher salt, cracked black pepper, garlic powder, and Italian seasoning. Lightly dredge each cutlet in the flour, shaking off all excess so only a sheer coating remains.

Sear until golden: Heat olive oil and 1 tablespoon butter in a large heavy skillet or cast-iron pan over medium-high heat. Once hot and shimmering, add chicken cutlets in a single layer. Sear undisturbed for 4 to 5 minutes per side until deeply golden and internal temperature reaches 165°F (74°C). Transfer chicken to a clean plate and tent loosely with foil.

Sauté garlic aromatics: Reduce heat to medium. Add remaining 2 tablespoons butter to the pan. Once foamy, stir in minced garlic and cook for 60 seconds until aromatic and pale golden, taking care not to scorch the garlic.

Deglaze the skillet: Pour in chicken broth and fresh lemon juice. Use a flat wooden spatula to scrape up all the caramelized browned chicken bits (fond) stuck to the pan bottom. Bring to a brisk simmer for 2 to 3 minutes until reduced by half.

Whisk in cream and parmesan: Turn heat down to medium-low. Slowly pour in heavy whipping cream and lemon zest, stirring gently. Bring to a low simmer (avoid boiling). Whisk in grated Parmesan cheese until melted and the sauce turns silky and coats the back of a spoon, about 2 minutes. Taste and adjust seasoning with a pinch of salt or pepper if needed.

Simmer cutlets and serve: Return the seared chicken cutlets and any collected plate juices back into the bubbling sauce. Spoon the velvety lemon garlic butter sauce all over each cutlet. Tuck lemon slices between the cutlets and simmer gently for 2 minutes until piping hot throughout. Sprinkle with fresh parsley and thyme, and serve immediately!