Preheat the oven to 425°.

Place the sliced peaches onto a rimmed baking sheet.

Sprinkle the brown sugar over the peaches and gently toss.

Roast the peaches until they begin to break down and turn golden, about 10 to 15 minutes.

Cool slightly and then transfer the peaches to a blender and puree.

You will get about 2 cups of really yummy peach puree.

Heat the half-and-half and vanilla in a saucepan over medium heat until little bubbles begin to form on the sides of the pan, about 5 to 6 minutes.

Remove the pan from the heat.

Heat the sugar in a separate saucepan with ¼ cup water over medium heat until the sugar dissolves, about 2 minutes.

Increase the heat and bring the sugar to a boil.

Continue boiling until the sugar begins to turn caramel in color, about 8 minutes.

Gently swirl the pan to make sure that the sugar colors evenly. Now, here is the tricky part. SLOWLY pour the warm half-and-half into the caramel. As it first blends, the hot caramel will bubble up and expand up the sides of the pan. Stop pouring until the bubbles settle down and then pour in the rest of the half and half.

Whisk the egg yolks in a small bowl.

Carefully pour about ¼ cup of the caramel/half and half into the eggs, whisking constantly. This will temper the egg yolks and help to prevent them from scrambling.

Pour the tempered egg yolks into the pan.

Reduce the heat to medium and stir until the caramel custard thickens enough to coat the back of a spoon, about 5 minutes.

Pour the custard through a fine sieve or colander into a clean bowl.

Stir in the peach puree.

Place that bowl into a larger bowl filled with ice cubes.

Chill the peach custard, stirring occasionally, until it comes to room temperature, about 20 minutes.

Cover the custard with plastic wrap and chill in the refrigerator for at least 4 hours.

Process according to the directions of your ice cream maker.