Rinse the dried samp under cold water to remove any impurities. Place the samp in a bowl, cover it with water, and let it soak overnight or for at least 8 hours. Drain the soaked samp before cooking.
Heat the vegetable oil in a large pot or Dutch oven over medium heat. Add the chopped onion and minced garlic, and sauté until they become translucent and fragrant.
Add the diced tomatoes and tomato paste to the pot, and stir to combine. Cook for a few minutes until the tomatoes start to break down and release their juices.
Add the drained samp to the pot, followed by the diced potatoes. Stir everything together to coat the samp and potatoes with the tomato mixture.
Sprinkle the ground cumin, paprika, dried thyme, salt, and pepper over the ingredients in the pot. Stir well to distribute the spices evenly.
Pour the vegetable or chicken broth into the pot, making sure it covers the samp and potatoes. If needed, add more broth or water to achieve the desired consistency.
Bring the mixture to a boil over medium-high heat, then reduce the heat to low and cover the pot with a lid. Let the stew simmer for about 1.5 to 2 hours, or until the samp and potatoes are tender. Stir occasionally to prevent sticking.
Once the samp and potatoes are cooked to your desired tenderness, remove the pot from the heat. Taste the stew and adjust the seasoning if needed.
Serve the samp and potato stew hot, garnished with fresh parsley or coriander, if desired. It pairs well with crusty bread or steamed vegetables.