Bring a large pot of salted water to a boil. Cook the ravioli according to package directions. Drain and set aside.
While the ravioli cooks, heat olive oil in a large skillet over medium heat. Add chicken, season lightly with salt and pepper, and cook for 4–5 minutes until golden and cooked through. Remove chicken from skillet and set aside.
In the same skillet, melt butter over medium-low heat. Add garlic and cook for 30 seconds, just until fragrant.
Reduce heat to low. Stir in heavy cream and Parmesan cheese, mixing until smooth and gently warmed.
Add cooked chicken back to the skillet, followed by the cooked ravioli. Toss gently to coat in the sauce. Use a splash of reserved pasta water if the sauce needs loosening.
Remove from heat and stir in fresh basil and red pepper flakes (if using).
Taste and adjust seasoning. Serve warm with extra Parmesan if desired.