First, heat olive oil over medium-high heat in a large soup pot. Then add the diced onion and garlic. Cook until the 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 and cook uncovered, for 12 minutes or until it has thickened. Be sure to stir occasionally.
Add the half and half or heavy cream and season to taste with salt and pepper.
Carefully transfer the soup to a blender, and puree it until there are no large chunks left.
Garnish with croutons and french bread on the side and serve hot.