Drain tomatoes in a large strainer or colander set over a large bowl, reserving the liquid. Stir the tomatoes and press firmly to remove as much liquid as possible. You should end up with about 4 cups of tomato juice. Set the tomatoes and the juice aside.
Heat the olive oil in a large pot or dutch oven over medium-high heat. Add the onion and carrots and cook until soft, about 4-5 minutes. Stir in ⅔ of the tomatoes, the bay leaf, and the brown sugar and cook until beginning to brown, about 10-15 minutes. Stir in the tomato paste and cook until starting to brown, about 1 minute.
Slowly stir in the reserved tomato juice, scraping up any browned bits on the bottom of the pot. Stir in the remaining tomatoes, baking soda, and salt. Bring to a boil, then reduce heat to medium low and simmer until slightly thickened, about 8 minutes.
Remove from heat and discard bay leaf. Use an immersion blender or blend in batches until smooth. Return soup to pot and stir in evaporated milk. Season with additional salt and freshly ground black pepper to taste. Serve hot.
You can use half regular and half fire roasted diced tomatoes if you wish for a smokier flavor.