Place potato cubes in a large pot and cover with cold water. Add 1 teaspoon salt to the water. Bring to a boil over high heat, then reduce to a simmer and cook until potatoes are tender when pierced with a fork, about 15-20 minutes.
While potatoes cook, place eggs in a medium saucepan and cover with cold water. Bring to a boil over high heat, then cover and remove from heat. Let stand for 12 minutes before transferring eggs to an ice water bath to cool completely.
Drain cooked potatoes and spread them in a single layer on a baking sheet to cool slightly. This helps prevent them from becoming mushy when mixed.
Peel the cooled eggs and separate yolks from whites. Place yolks in a medium bowl and mash with a fork until smooth. Finely chop the egg whites and set aside.
To the mashed egg yolks, add mayonnaise, Dijon mustard, yellow mustard, white vinegar, paprika, and garlic powder. Whisk until completely smooth and creamy.
In a large mixing bowl, combine cooled potatoes, chopped egg whites, red onion, and chives. Gently fold in the creamy yolk mixture until everything is evenly coated.
Season with salt and black pepper to taste. Cover and refrigerate for at least 1 hour to allow flavors to meld together.
Before serving, give the salad a gentle stir and garnish with additional chives and a sprinkle of paprika.