
Get ready. Preheat your oven to 450°F.
Roast the carrots and tomatoes. In a large mixing bowl, toss the tomatoes and carrots with a generous drizzle of olive oil and a pinch salt and pepper. Transfer to a large baking sheet and spread well in one layer. Roast in the heated oven until the tomatoes have deflated and began to char at the edges, about 30 minutes. Set aside for about 10 minutes to cool.
Blend. Transfer the roasted carrots and tomatoes (along with their skin and seeds) to the bowl of a food processor fitted with a blade. Add a splash of water and blend until the vegetables have broken down and combined. Some texture is nice, so stop the processor before it becomes a super smooth puree.
Sauté the onions and garlic. In a large pot, heat 2 tablespoon of olive oil over medium-high heat. When the oil begins to shimmer, add the onions and cook, stirring, until softened, about 3 minutes. Add the garlic and cook briefly until golden, about 1 minute.
Add the tomatoes and reduce. Pour the roasted tomato mixture into the pot with the onions. Stir in the crushed tomatoes, basil, thyme, oregano, paprika, cumin, and 2 1/2 cups of water. Season with salt and pepper. Bring to a boil, then lower the heat and cover, leaving the lid slightly ajar to allow some steam to escape. Let simmer for about 20 minutes or so.
Finish and serve. Remove the thyme springs and transfer the soup to serving bowls. If you like, add top each serving with a squeeze of fresh lime and a generous drizzle of extra virgin olive oil. Optionally, serve with your grilled bread, grilled cheese, or crusty bread on the side. Enjoy!