Preheat oven to 425°F. Place potatoes, rosemary sprigs, smashed garlic, 1/4 cup of the salt, and water to cover in a 3-quart saucepan. Bring to a boil over high; reduce to medium, and simmer until potatoes are tender when pierced with a fork, 10 to 15 minutes. Drain; discard rosemary sprigs and smashed garlic.
Brush a rimmed baking sheet with 2 tablespoons of the oil. Arrange potatoes on prepared baking sheet. Using the heel of your hand, lightly crush potatoes until they are about 1/2 inch thick. Brush with 1 tablespoon of the oil. Bake in preheated oven until golden brown and crisp, 25 minutes.
Stir together butter, chopped parsley, thyme, rosemary, minced garlic, pepper, and remaining 1 tablespoon oil and 1/2 teaspoon salt. Brush mixture over potatoes, and serve immediately.