Preheat oven to 350°F (175°C) and line two baking sheets with parchment.

Cream the butter and sugar until pale and fluffy, about 2 minutes. Mix in the melted ice cream until smooth.

Fold in the self-rising flour with a spatula just until the flour disappears. The dough will be soft and glossy.

Drop dough by 1.5-tablespoon scoops onto the sheets, spacing them 2 inches apart.

Bake one sheet at a time for 10 to 12 minutes, until edges are set but centers still look soft.

Let cookies rest on the sheet for 3 minutes, then transfer to a wire rack to cool completely.