Peel and dice the potatoes. Add the potatoes to a large pot along with a generous pinch of kosher salt. Place over high heat and bring to a boil. Cook the potatoes for 15 to 20 minutes until tender. When the potatoes are tender, drain and return to the pot. Mash the potatoes, then transfer to a mixing bowl and allow to cool.
To prepare the leeks, cut off the dark leaves from the top. Trim the root and wash between the layers. Chop into a small dice. Melt the butter in a skillet over medium heat. Add the leeks and sauté for 4 to 5 minutes until very tender.
Combine the mashed potatoes and sautéed leeks. Add 1 egg along with 1 tsp kosher salt and ¼ tsp pepper to the potatoes. Mix until well combined. Chill until cold.
The croquettes will be easier to shape when cold. Using wet hands, scoop up a golf ball sized amount of the filling. Press out flat on the palm of one hand and place a cube of mozzarella on top. Bring up the edges and cover the cheese. Gently roll the ball around to smooth the edges. Transfer to a baking sheet and chill until ready to bread the croquettes.
Set up a standard breading station with the all-purpose flour in the first container. In the second container, whisk the remaining 2 eggs together with the water. Add the panko crumbs to the third container.
Take one of the croquettes and roll in the flour. Shake off the excess and then roll in the egg mixture. Let the excess egg drip off and then transfer to the crumbs. Roll the croquette in the crumbs, gently pressing to ensure the crumbs adhere but being careful not to crush it. Transfer to a plate and repeat with the remaining croquettes.
Once the croquettes are all breaded, you can add an optional second coat. Double breading the croquettes will give them a smooth, round appearance. Roll each croquette in the egg mixture again followed by the crumbs. Store in the fridge until you’re ready to fry them.
Preheat the oven to 300°F. Line a baking sheet with a rack or paper towel. Fill a deep pot with about 3 inches of vegetable oil. Heat over medium heat until the oil reaches 325°F / 162°C. Carefully lower the croquettes into the hot oil with a slotted spoon. Fry about 5 to 6 croquettes at one time. Gently stir the croquettes with a slotted spoon while frying so they brown evenly.
Fry the croquettes for 5 to 7 minutes until well browned. Remove from the oil with a slotted spoon onto the prepared baking sheet. Repeat with the remaining croquettes until they are all cooked. Keep the cooked croquettes warm in the oven while frying the rest.
In a small bowl, combine the sour cream, chives, the remaining ½ tsp kosher salt, and ¼ tsp pepper. Stir together and refrigerate before serving.
To serve, transfer the croquettes to a platter. Sprinkle with chopped chives and serve with the dipping sauce. Enjoy!