Preheat the oven to 300 degrees F, and line a baking sheet with parchment paper. Slice the tomatoes in half and place them on the baking sheet, cut side facing up. Drizzle a little olive oil over them, and sprinkle with salt. Roast for 2 hours or until the top surface of the tomatoes is puckered and somewhat dry. Remove and set aside.
Increase the oven temperature to 425 degrees F. Slice off the tops of the carrots, and quarter them lengthwise. Toss in a little olive oil, lightly sprinkle with salt, and lay on a baking sheet lined with parchment paper. Roast for 15 minutes. Turn the carrots over and roast for another 15 minutes. The carrots should be slightly caramelized. Remove from the oven and set aside.
Bring one quart of water to a boil in a large pot over high heat. Remove from the heat, and add all of the dried chiles to the hot water. Place the lid on the pot and let the chiles soak for one hour, or until soft. Remove from the water, tear off the tops and remove the seeds. Set aside.
Combine the dried tomatoes (if using), coriander seed, caraway seed and kosher salt in a spice grinder, coffee grinder, or mortar and pestle and grind to a coarse powder.
Combine the roasted tomatoes, carrots, softened chiles, and ground spices in the bowl of a food processor fitted with a blade and whirl like crazy until a thick paste develops. Add the vinegar, olive oil and water and whirl again until completely incorporated.
Store in an airtight jar covered with a little olive oil in the refrigerator