Chicken and Pasta With Lemon Pesto

1 (16-ounce) package linguine or spaghetti pasta

2 tablespoons unsalted butter

2 tablespoons olive oil

3 cloves garlic (minced)

5 boneless, skinless chicken breasts (cubed)

1/2 teaspoon salt

1/8 teaspoon white pepper

1 cup heavy cream

1 (9-ounce) package basil pesto, 3 tablespoons set aside

1/4 cup freshly squeezed lemon juice, 1 tablespoon set aside

1 teaspoon grated lemon zest

2 cups frozen baby peas

1/3 cup freshly grated Parmesan cheese