In a heavy bottomed pot or dutch oven, heat olive oil over medium-high heat.
Add diced onion and garlic. Cook, stirring as needed, until onion is translucent - about 5-8 minutes.
Add the San Marzano peeled tomatoes, including the juice, vegetable stock, dried oregano, dried basil and sugar. Season with salt and pepper and stir to combine. Bring to a low simmer. Cook uncovered, for 12 minutes or until it has thickened. Stir occasionally.
Add the half and half or heavy cream and season to taste with salt and pepper.
Using an immersion blender (or carefully transfer soup to a blender), puree soup until there are no large chunks left.
Serve immediately garnished with croutons and french bread on the side.
Store in an airtight container in the fridge for up to 5 days or you can freeze the soup for up to 3 months.