In a large Dutch oven, combine the olive oil and butter and place over medium heat to melt the butter. Add the onion and carrot. Cook with the lid partially covering the pot and stir frequently until the vegetables softened, about 8 minutes. Stir in the garlic and cook for another minute.

Add the tinned tomatoes. Pour a little of the chicken stock into the cans, and swirl it around to get the rest of the tomato juices out, then add it to the pot. Pour in the remaining broth and stir in the black pepper.

Bring to a boil. Reduce the heat to medium-low and continue simmering for 30 minutes, stirring occasionally. Remove from the heat.

Using a stick blender, blitz the soup to break up the tomatoes until chunky or puree until smooth. You can also break up the tomatoes with a potato masher. Taste and season with salt as needed. If the soup is very acidic or the tomatoes are lacking in a bit of flavor, stir in the sugar. Serve topped with fresh basil and black pepper.