Melt butter and olive oil in a saucepan over medium-low heat. Add cream, garlic, and white pepper; bring to just under a boil. Reduce heat and simmer, stirring often, until mixture is slightly reduced, about 5 minutes.
Stir Parmesan cheese into the cream mixture and simmer until sauce is thickened and smooth, 8 to 10 minutes. Add mozzarella cheese to sauce; cook and stir until cheese is melted about 5 minutes.
Bring a large pot of lightly salted water to a boil. Cook pasta in the boiling water, stirring occasionally until cooked through but firm to the bite. Drain and transfer pasta to serving plates. Spoon sauce over pasta.