Step 1Heat the broiler. Core the bell peppers and place them, skin-side up, on a baking sheet. Drizzle over 2 tablespoons oil and season with a generous pinch of salt and pepper. Broil the peppers until they are well-charred but not burnt, 3 to 5 minutes depending on the heat of the broiler.
Step 2Heat a grill or grill pan over medium-high heat until hot. Meanwhile, peel the onions and halve them lengthwise. Coat the onions with 1 tablespoon canola oil and season with a pinch each of salt and pepper. Grill the onions on all sides until well-charred. Set aside until cool enough to handle, then trim off the root end and coarsely chop the onions.
Step 3In a large, heavy-bottomed pot, heat the remaining 2 tablespoons of oil over medium-high heat until hot. Add the onions and stir around the pot for a minute to soften, then add the carrots. Cook, stirring occasionally, until the onions are translucent. Stir in 2 teaspoons of salt and one-half teaspoon of pepper, along with the garlic. Continue to cook, stirring frequently, until the carrots are softened slightly and the garlic is aromatic, 1 to 2 minutes.
Step 4Stir in the tomatoes and peppers. Cook, stirring frequently, for about 10 minutes to develop the flavors. Add the water and bring the soup to a simmer. Reduce the heat to a gentle simmer, loosely cover the pot and cook for 45 minutes.
Step 5Blend the soup using an immersion blender, or in batches using a stand blender, and strain. Add the sherry vinegar, and season to taste with salt and pepper. This makes a generous 2 quarts soup.