Add the potatoes to a large pot of water with 1 tsp of salt. Bring to a low boil for 15-20 minutes or until the potatoes are soft. Strain the water and let the potatoes cool once done cooking.
In a medium-sized pot, add water, 1 tsp salt, and 1 tsp baking soda. Bring to a boil. Add the eggs and cook for 12 minutes. Once done cooking, remove the eggs and place them into a bowl filled with ice and water for 10 minutes. After cooling, peel and chop 8 eggs into bite-size pieces. Place them into a large bowl. For the last egg, cut it in half from top to bottom and set it aside.
Add the rest of the ingredients to the large bowl with the chopped eggs. Gently toss. Once the potatoes are cool, fold them into the mixture. Taste and adjust any seasoning.
Clean the sides of the bowl. Place the last egg in the middle with the yolk side facing up. Sprinkle with smoked paprika.
Refrigerate for 12 hours for the best results.