Heat butter and olive oil in a saucepan over medium-low heat until butter is melted. Mix in cream, garlic, and white pepper and bring to a simmer, stirring often, 3 to 5 minutes.
Stir in Parmesan cheese and simmer, stirring frequently, until sauce has thickened and is smooth, 8 to 10 minutes. Add mozzarella cheese once sauce has thickened and stir until smooth.
