Heat a large cast iron skillet and add the canola oil. When the oil begins to smoke lightly, add the tomatoes in a single layer. Season with salt, to taste, and add the sugar. You want to blister the skin slightly, drawing out water from the tomatoes, to intensify their flavor. Add the vermouth. Continue cooking on low heat.
In a soup pot, heat 1 tablespoon of the olive oil and add the garlic, shallots, and red pepper flakes. Season with salt and pepper. Add the oregano and stir to blend. Allow to cook, over low heat, until the shallots and garlic become tender and translucent, 3 to 5 minutes. Add the canned tomatoes and the water. Turn the heat down to medium and cook until the tomato flesh starts to lose shape, 12 to 15 minutes. At this point, the soup should be mushy and blender-ready. If there are still some hard pieces, add a little more water and cook for a few additional minutes. Taste for seasoning.
Put about half of the tomato soup in the blender and puree until smooth. Next, puree the roasted Roma tomatoes in the blender until smooth, adding the remaining olive oil through the top in a slow, steady stream. Taste for seasoning. Add both back to the remaining chunky soup. Taste for seasoning.
On a flat surface, slice bread into 4 by 1/2-inch thick slices. Tear each piece into a freeform shape that sits nicely across the top of your soup bowls (the nice torn edges will get super crispy). Set on a sheet tray and toast in oven for 4 to 5 minutes until lightly golden and crispy.
Ladle the soup into crocks or small oven-proof bowls. Top with 1 piece of toasted bread per bowl. Finish with some shredded mozzarella and broil until golden brown, about 2 minutes.