Pat chicken breasts dry and cut each in half horizontally to create 4 thin filets. Season both sides with salt and pepper, then dredge in flour and shake off any excess.

Heat 1 tablespoon butter and olive oil in a large skillet over medium-high heat. Sear chicken for 10 to 12 minutes total, flipping once or twice, until deep golden brown and cooked through to 165 degrees F. Transfer to a plate. Do not wipe the skillet.

Reduce heat to medium. Add remaining 2 tablespoons butter to the skillet. Cook diced onion and minced garlic for 1 to 2 minutes, stirring often, until fragrant. Do not let the garlic burn.

Add chopped artichoke hearts and fresh baby spinach. Cook for 3 to 4 minutes, stirring occasionally, until spinach is fully wilted and artichokes are lightly browned at the edges.

Pour in chicken broth and scrape up browned bits from the pan bottom. Simmer for 2 to 3 minutes until reduced by about half.

Reduce heat to low. Stir in sour cream until fully smooth, then add heavy cream. Let warm through gently for 1 to 2 minutes without boiling. Stir in Parmesan cheese and season to taste with salt and pepper.

Return seared chicken to the skillet and spoon sauce over each piece. Simmer on low for 2 minutes until warmed through. Serve immediately with extra Parmesan cheese on top.