In a skillet with tall sides, heat a drizzle of olive oil over medium-high heat. Season both sides of the chicken with salt and pepper. Cook the chicken for about 5 minutes on each side, or until golden brown and cooked through. Remove chicken to a plate and set aside.
Bring a pot of water to a bowl, then boil the tortellini according to package directions.
In the same skillet that you cooked the chicken, add the butter and garlic. Reduce the heat to medium and cook until the butter is melted, then whisk in the flour and cook for one minute. Pour in the milk and whisk until thickened, about 2-3 minutes. Whisk in the cream cheese until smooth. Add the heavy cream, pesto and parmesan. Simmer until thickened, about another 2-3 minutes.
Add the cooked tortellini and chicken to the pesto cream sauce. Simmer until the chicken is warm, about 3-5 minutes.
Serve with fresh basil and more pesto, if desired!