1. In a medium saucepan, combine the heavy cream, milk, and granulated sugar. Heat over medium, stirring occasionally, until the sugar has dissolved and the mixture begins to steam, about 5 minutes.

2. In a separate bowl, whisk the egg yolks. Slowly pour in about 1/2 cup of the hot cream mixture, whisking constantly, to temper the yolks.

3. Pour the tempered yolks back into the saucepan with the remaining cream mixture. Cook, stirring constantly with a wooden spoon or spatula, until the mixture thickens enough to coat the back of the spoon, about 5-7 minutes.

4. Remove from heat and stir in the chopped peaches. Strain the mixture through a fine-mesh sieve, pressing on the solids to extract as much liquid as possible.

5. Transfer the peach-infused custard to a clean bowl and refrigerate until completely chilled, about 2 hours.

6. In a medium bowl, combine the flour, brown sugar, butter, and cinnamon. Use your fingers to work the butter into the dry ingredients until the mixture resembles coarse crumbs.

7. Churn the chilled custard in an ice cream maker according to the manufacturer’s instructions. During the last 5 minutes of churning, add the crumbled cobbler topping and continue churning until fully incorporated.

8. Transfer the ice cream to a freezer-safe container and freeze for at least 2 hours before serving.