Heat olive oil in a large soup pot over medium-high heat.
Add chopped onion and crushed garlic. Cook, stirring often, until softened, about 10 minutes. Be careful not to burn the garlic.
Add the ground peeled tomatoes and stock to the pot.
Bring mixture to a boil, then reduce heat to maintain a simmer.
Cook until soup is slightly thickened, about 20 minutes.
Season with salt and pepper to taste.
Stir in the sliced fresh basil.
Place the pot of soup directly in the sink and use a stick blender to blend until smooth.
Serve immediately.