Scrub the potatoes and cut them into 1/2-inch dice. Put the diced potatoes in a medium saucepan and cover them with water. Add the 1 1/2 teaspoons of kosher salt and bring the potatoes to a boil over high heat. Cook the potatoes for about 5 minutes, or just until they are slightly softened. Drain well.

Melt 1 tablespoon of butter in a large skillet over medium heat. Add the onions to the skillet along with a dash of kosher salt. Sauté the onions until softened, about 4 minutes. Remove the onions to a plate and set them aside.

Add the remaining 3 tablespoons of butter to the skillet and add the potatoes. Cook over medium heat for about 5 to 7 minutes, until browned on the bottom; flip and continue cooking to brown the other side, about 5 minutes longer.

Add the cooked onions, paprika, and pepper to the potatoes; stir to combine. Taste and add kosher salt, as needed.

Remove the skillet from the heat and serve immediately.