Place the baby new potatoes in a large pot and cover with cold water. Add salt to make the water salted, bring to a boil, then reduce heat and simmer until a fork or skewer slides into the potatoes easily (about 15–20 minutes, depending on size). Drain and set the potatoes aside.
Return the empty pot to the stove over medium heat and add the salted butter. Melt the butter.
Add the minced garlic to the melted butter and cook, stirring, about 30 seconds, until fragrant but not browned.
Remove the pot from the heat and stir in the sour cream until smooth.
Add the drained potatoes back to the pot. Season with salt and pepper to taste. Gently toss or stir, crushing a few potatoes slightly with the back of a spoon to help thicken the sauce.
Stir in the chopped fresh dill and chopped fresh parsley. Taste and adjust seasoning if needed, then serve warm.