Begin by washing the baby red potatoes thoroughly to remove any dirt. Cut them into 1-inch pieces; you can quarter or cut them into 1/8ths if they are larger.
In a large pot, fill it with water and add 1 teaspoon of salt. Bring the water to a rolling boil, then add the cut potatoes. Cook the potatoes for about 10-15 minutes, or until they are tender when pierced with a fork. Be careful not to overcook them.
Once cooked, drain the potatoes in a colander and let them sit for a few minutes to allow excess moisture to evaporate.
In a large skillet, melt 4 tablespoons of unsalted butter over medium heat. Add the drained potatoes to the skillet, sprinkle with garlic salt to taste, and gently toss to coat the potatoes.
Add 2-3 tablespoons of freshly chopped dill and 1/3 to 1/2 cup of shredded Parmesan cheese. Toss gently until well combined and the cheese starts to melt.
Transfer the Buttered Red Potatoes with Dill to a serving dish. Garnish with an additional sprinkle of fresh dill and serve warm.