Apple Galette

Melt the butter in a small saucepan over medium heat. Using a slotted spoon, transfer the apples to the saucepan; reserve their juices in the bowl. Cover the pan and cook the apples, stirring every 2 minutes, until all their juices evaporate and the apples are tender, about 6 minutes. Uncover the apples, add 1/2 tablespoon sugar, and cook, stirring, until the sugar dissolves and is absorbed, 1 minute. Repeat this three more times, adding another 1/2 tablespoon sugar each time and cooking for 1 minute after each addition. Finally, add the reserved juices from the bowl and continue cooking until the syrup absorbs into the apples and the sauce is smooth, about 30 seconds more. Transfer the compote to a bowl and let cool. Cover with plastic wrap and refrigerate until cold, at least 1 hour.