Start with the dressing: Add the tomatoes, oil, garlic, miso, bay leaves, cardamom shells and seeds, paprika and a heaping ¼ teaspoon salt to a large (lidded) sauté pan. Place over medium-high heat, give everything a good stir and leave it, uncovered, until it starts to bubble gently.
Once bubbling, turn the heat down to medium-low, cover with the lid and cook gently for 15 minutes, stirring once, until the tomatoes have burst and start to release their juices. Turn down the heat if necessary; you want the garlic to soften without taking on color, and you want the tomatoes to not completely disintegrate. Stir in the lime juice and set aside.