To make a homemade red pizza sauce from scratch, heat 2 tablespoons of olive oil in a large skillet or saucepan until it shimmers. Stir in 1 clove of crushed garlic and one 28-ounce can of tomato puree. Add 1 teaspoon of dried marjoram and 1 teaspoon of dried basil.
Season the sauce with salt and freshly ground pepper, to taste. Cover the pan and bring the mixture to a boil, then reduce the heat and simmer the sauce for 30 minutes.
Alternatively, to make a creamy Parmesan pizza sauce, melt 1 tablespoon of butter in a saucepan over medium heat. Add 1/3 cup of onion and 2 cloves of chopped garlic to the pan, and cook the mixture until the onion becomes soft and translucent. Stir in 1 tablespoon of all-purpose flour and 1/8 teaspoon of white pepper, 1 cup of milk and 1/4 teaspoon of instant chicken bouillon granules. Stirring occasionally, heat the mixture until it becomes thick and bubbly. Add 1/4 cup of grated Parmesan cheese, and stir the mixture until the sauce is smooth.
To create a classic pesto sauce for pizza, add 2/3 cup of extra-virgin olive oil, 2 cups of packed fresh basil leaves, 2 cloves of peeled garlic and 1/4 cup of pine nuts to a food processor. Pulse the ingredients until the mixture is smooth. Season the pesto with salt and pepper, to taste. Transfer the pesto to a bowl, and stir in 1/2 cup of freshly grated Pecorino cheese.