Cut each chicken breast in half horizontally to form two thin pieces. Pound lightly, if needed, to ensure even thickness. Season both sides with salt and pepper.
Heat oil in a large skillet over high heat. Once hot (the chicken should sizzle on contact), add chicken in a single layer. Cook for 4–6 minutes total, flipping once halfway through. Add the butter to the pan when you flip the chicken. Cook until golden and cooked through, then transfer to a plate and cover with foil.
In the same pan, add garlic. Sauté for 15 seconds, just until fragrant. Don’t let it burn. Add chicken broth and bring to a simmer, scraping up browned bits from the pan. Let simmer for 1 minute until slightly reduced.
Whisk in the cream, Parmesan, pesto, Dijon mustard, and lemon juice. Bring to a gentle simmer. Reduce heat to medium and cook for 2–3 minutes, stirring often, until thickened and smooth. Stir often to ensure Parmesan fully melts into the sauce.
Taste and adjust salt and pepper if needed. Stir in fresh basil (if using), then return chicken and any juices to the pan. Spoon sauce over the top and let simmer for 1 more minute. Add a sprinkle of Parmesan on top, if desired.
Serve immediately with crusty buttered bread on the side for dipping.
Video
Notes
Note 1: Use freshly grated Parmesan or store-bought finely shredded (thin batons). Avoid powdery, sand-like Parmesan; it doesn't melt right. I grab a block of Parmesan and grate it with a microplane for the best texture! Gently pack in the measuring cup.Note 2: Use a high-quality store-bought pesto or homemade. I like Rana's basil pesto best for store-bought.Storage: Best eaten fresh. Store leftovers in an airtight container in the fridge for up to 3 days. Reheat gently on the stove over low heat.