Season the chicken breasts and shrimp with salt and black pepper.
In a large skillet over medium-high heat, add the olive oil and 1 tablespoon of butter.
Sear the chicken breasts for 5-7 minutes per side until they reach an internal temperature of 165°F (74°C). Remove from skillet and tent with foil.
In the same skillet, add 1 tablespoon of butter and the shrimp. Sauté for 2-3 minutes until pink and opaque. Add half of the minced garlic during the last 30 seconds. Remove shrimp and set aside.
Add the remaining 2 tablespoons of butter and the remaining garlic to the pan, cooking for 1 minute until fragrant.
Pour in the chicken broth to deglaze the pan, scraping up any browned bits from the bottom.
Whisk in the heavy cream, lemon juice, lemon zest, and red pepper flakes. Bring to a gentle simmer for 3-5 minutes until the sauce slightly thickens.
Stir in the Parmesan cheese until melted and smooth.
Fold in the fresh basil chiffonade.
Return the chicken and shrimp to the skillet, spooning the sauce over the proteins to coat thoroughly. Serve immediately.