Step 1 Cut the peaches into very small pieces. The smaller you cut them, the faster they will freeze and the finer the final texture will be. Arrange the peach pieces in a single layer on a rimmed cookie sheet and freeze solid, about 2 hours.
Step 2 Put the frozen peach pieces in a food processor with the sugar and grind briefly. Add the mascarpone and pulse until the mixture is smooth.
Step 3Empty the food processor into a small container and freeze again, 20 to 30 minutes, before serving. If the ice cream freezes solid, simply process it briefly again before serving.