Melt 4 1/2 tablespoons butter in a large skillet over medium-high heat. Cook potatoes in butter, stirring occasionally, until golden brown, 10 to 15 minutes.

Meanwhile, melt remaining 1 1/2 tablespoons butter in a small skillet over medium heat; cook and stir onion and garlic in butter until onions are tender, about 5 minutes.

Stir onion mixture into potatoes. Cook and stir until potatoes are tender, about 10 more minutes.