In a large mixing bowl, whisk together 2 cups of heavy cream, 1 cup of sweetened condensed milk, and 1 teaspoon of vanilla extract until well combined. Cover the mixture with plastic wrap and chill it in the refrigerator for at least 2 hours, or overnight for best results.

In a medium saucepan, combine 4 cups of diced ripe peaches, ½ cup of granulated sugar, and 1 teaspoon of vanilla extract. Cook over medium heat, stirring frequently, until the mixture thickens and bubbles, about 15-20 minutes. Allow the compote to cool completely.

Preheat your oven to 350°F (175°C). In a mixing bowl, blend ¼ cup of melted unsalted butter with ½ cup of sugar, 1 teaspoon of vanilla extract, and ½ cup of whole milk. Gradually mix in 1 cup of all-purpose flour, 1 tablespoon of baking powder, and a pinch of salt until smooth. Spread the batter onto a greased baking sheet and bake for 13-15 minutes.

Once the ice cream base has chilled, pour it into your ice cream maker. Churn according to the manufacturer's instructions for about 30-40 minutes, or until the mixture reaches a thick, soft-serve consistency.

In a large bowl, gently fold together half of the cooled peach compote and a third of the crumbled cobbler pieces into the churned ice cream. Layer half of this mixture into a freezer-safe pan, drizzling with salted caramel sauce, then add the remaining peach compote, another third of the cobbler, and finish with the last of the ice cream mixture. Freeze for 2 hours or until solid.