Prep the chicken: Pat chicken dry and season lightly with salt, pepper, and a pinch of smoked paprika if using. If breasts are thick, pound to an even 1/2–3/4 inch so they cook evenly.
Sear the chicken: Heat olive oil and butter in a large skillet over medium-high.
Add chicken and sear 4–5 minutes per side until golden. Transfer to a plate; it will finish cooking in the sauce.
Soften aromatics: Reduce heat to medium. Add onion and cook 2–3 minutes until translucent.
Stir in garlic for 30 seconds until fragrant.
Build the base: Pour in chicken broth, scraping up browned bits. Whisk in the ranch seasoning and Dijon. Simmer 2–3 minutes to slightly reduce.
Add the cream: Lower heat to medium-low.
Stir in heavy cream and sour cream (or Greek yogurt). Keep the heat gentle so the sauce stays smooth.
Thicken and enrich: If using, stir in Parmesan until melted. Taste and adjust seasoning with pepper and salt as needed.
Finish the chicken: Nestle chicken back into the sauce.
Simmer on low 5–7 minutes, flipping once, until chicken reaches an internal temperature of 165°F (74°C).
Add greens: Fold in spinach or kale until wilted, 1–2 minutes. Remove from heat.
Garnish and serve: Top with chopped chives or parsley. Serve with mashed potatoes, rice, crusty bread, or roasted veggies to soak up the sauce.