Preheat oven to 390°F and line a baking sheet with aluminium foil.
Take a sieve and position it above a mixing bowl. Pour the crushed tomatoes into the sieve and drain all the liquid into the bowl. Push the tomatoes against the sieve with the back of a spoon to thoroughly remove all of their liquid. Scoop the tomatoes onto the prepared baking sheet. Drizzle the ¼ cup olive oil over the tomatoes and season with salt and pepper. Roast in the oven for 10 minutes until caramelised. Keep an eye on the tomatoes -- you don't want them to burn. Keep the reserved tomato liquid aside.
In a large saucepan over medium-high heat, heat 3 tablespoons olive oil. Add the celery, carrot, onion and garlic and sauté for 8 to 10 minutes until soft but not golden. Add the reserved tomato juices, broth, roasted tomatoes and bay leaves and bring the mixture to boil. Reduce heat to low and simmer for 20 minutes until all vegetables are soft.
Remove the bay leaves, add basil, and purée with a handheld blender until smooth.