Preheat the oven to 450 degrees F.
Place the potatoes in a large pot and fill it with cold water. Bring the water to a boil. Simmer the potatoes until they are just barely fork tender. Strain the potatoes and let them cool slightly.
Brush a baking sheet with 1 1/2 tablespoons of olive oil. Place the potatoes on the sheet. Use a fork or potato mashed to smash them once, keeping them in one piece. Drizzle the remaining olive oil over the potatoes. Sprinkle with the salt, pepper and garlic. Place the sheet in the oven and roast the potatoes for 25 to 30 minutes, until golden and crispy.
While the potatoes are roasting, melt the butter. Stir the rosemary into the butter.
When the potatoes are finished, drizzle each of them with the rosemary butter. Top each with a piece of the burrata cheese.