Pat the lamb shanks dry. In a shallow bowl, combine 1 tablespoon kosher salt, 2 teaspoons garlic powder, 2 teaspoons ground cumin, 1 teaspoon ground coriander, 1 teaspoon ground mustard and 1/2 teaspoon freshly cracked black pepper. Rub the spice mixture all over the shanks. Let the shanks come to room temperature, about 30 minutes.

Preheat the oven to 325°F (160°C).

Heat a large Dutch oven over medium-high heat and add 2 tablespoons neutral oil. When the oil is hot and shimmering, sear the shanks in batches without crowding the pot (for three shanks: sear two, then the remaining one). Brown each shank about 5–7 minutes per side, until deeply browned. Transfer seared shanks to a plate.

Lower the heat to medium. Add the sliced 1/4 white onion to the Dutch oven and cook, stirring occasionally, until softened, about 3–4 minutes. Add the 2 cloves garlic and cook until fragrant, about 30–60 seconds.

While the onion softens, combine the 15-ounce can whole or diced tomatoes (with their juices), 1 chipotle in adobo, and 1 cup water in a blender. Blend until smooth, about 1 minute.

Pour the blended tomato–chipotle mixture into the Dutch oven and scrape up any browned bits from the bottom. Add the 4 roughly chopped carrots and stir to combine. Bring the mixture to a gentle simmer on the stovetop.

Nestle the seared lamb shanks back into the sauce so they are at least partially submerged. Cover the Dutch oven with its lid and transfer it to the preheated oven. Braise for 2½ to 3 hours, until the lamb is fork-tender.

Remove the Dutch oven from the oven. Transfer the lamb shanks to a serving platter and tent with foil to keep warm. Return the Dutch oven to the stovetop over medium-high heat and simmer the sauce, uncovered, until it thickens to your liking, about 10–15 minutes.

Return the shanks to the sauce or spoon the sauce and carrots over them. Garnish with 1 tablespoon minced cilantro, thinly sliced radish, diced white onion (as desired), and lime wedges. Serve hot.