Peel the potatoes and cut them into wedges. Add about 4 cups water (1 liter) to a pot, then add the potatoes and bring to a boil. Add the fish as well. Remove the fish and potatoes as soon as each is cooked—they may finish at different times. If you want to add rice, add it with the potatoes and cook for about 20 minutes, until the rice is done.

Meanwhile, place the eggs in a saucepan and cover with water. Bring to a boil, then cook for 10 minutes. Some people cook the eggs with the potatoes, but I prefer not to, since you never know what might be on the eggshells.

If the shrimp are raw, cook them in the same water used for the potatoes and fish to add more flavor. Once cooked, peel the shrimp and set aside.

To make the mayonnaise, place the egg and oil in a blender cup. Insert the immersion blender all the way to the bottom and turn it on, keeping it at the bottom until the oil is fully incorporated and the mixture is thick. Gently move the blender up and down to emulsify the mayonnaise. Add a little lemon juice and salt to taste.

Once the broth has cooled slightly, gradually add about 3/4 cup (200 ml) of the broth to the mayonnaise, straining the broth if needed. Blend with the immersion blender as you add the broth. If the broth is too hot, it can cause the mayonnaise to separate.

Add the mayonnaise mixture to the remaining broth along with all the previously cooked ingredients. From this point on, do not let the soup boil, as this can cause the mayonnaise to separate and make the soup look unappetizing.

Serve the gazpachuelo with half a hard-boiled egg on top.