Begin by washing the baby red potatoes thoroughly under cold running water. Cut them into 1-inch pieces, quartering them or cutting them into 1/8ths if they are larger.
In a large pot, bring water to a boil and add 1 teaspoon of salt. Once boiling, carefully add the cut potatoes. Cook for about 15-20 minutes, or until the potatoes are fork-tender.
Once cooked, drain the potatoes in a colander and return them to the pot.
While the potatoes are still warm, add the 4 tablespoons of unsalted butter. Allow it to melt and coat the potatoes. Then, sprinkle garlic salt to taste.
Now, add the chopped fresh dill and Parmesan cheese to the pot. Gently toss everything together until the potatoes are well coated.
Transfer the Buttered Red Potatoes with Dill to a serving dish, and garnish with extra dill or Parmesan if desired. Serve warm.