Heat the olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper. Cook the chicken for 6-7 minutes per side, or until golden brown and cooked through. Remove the chicken from the skillet and set it aside.
In the same skillet, melt the butter over medium heat. Add the minced garlic and sauté for 1-2 minutes, until fragrant. Pour in the chicken broth and bring it to a simmer. Let it reduce for 2-3 minutes.
Add the heavy cream to the skillet, stirring well to combine. Bring the mixture to a simmer and cook for 3-4 minutes, allowing the sauce to thicken. Stir in the chopped fresh basil and grated Parmesan cheese.
Return the cooked chicken to the skillet, spooning the sauce over the top. Simmer for an additional 2-3 minutes, allowing the chicken to soak up the flavors. Serve with a garnish of fresh basil and a squeeze of lemon juice.