In a bowl, whisk together the heavy cream, sweetened condensed milk, vanilla essence, salted caramel sauce, and sea salt until well combined. Transfer to the refrigerator to chill for at least 2 hours—this resting time allows the flavors to meld and ensures the mixture churns properly. I find that chilling overnight actually gives you a smoother, creamier final texture, so do this step first thing if you're planning ahead.
In a pot, combine the peeled and sliced peaches, 1/2 cup sugar, 2 tsp vanilla essence, lemon juice, and ground cinnamon. Cook over medium heat for 15-20 minutes, stirring occasionally, until the peaches break down and the mixture becomes thick and syrupy. The lemon juice brightens the peach flavor and the cinnamon adds warmth—don't skip it! Once thickened, transfer to a bowl and let cool completely to room temperature before proceeding.
Preheat your oven to 350°F. In a bowl, whisk together the melted butter, 3/4 cup sugar, 2 tsp vanilla essence, and milk until smooth. In a separate bowl, combine the flour, baking powder, and salt, then fold the dry ingredients into the wet mixture until just combined—don't overmix. Spread the batter on a sheet pan and bake for 13-15 minutes until golden and a toothpick inserted in the center comes out clean. Let cool completely, then break into bite-sized pieces.
Remove the chilled cream mixture from Step 1 and pour it into an ice cream machine. Churn according to your machine's instructions, typically 35-40 minutes, until the mixture reaches a soft-serve consistency. The churning process incorporates air and prevents large ice crystals from forming, giving you that smooth, creamy texture.
Working quickly, fold half of the cooled peach mixture from Step 2 and half of the cake pieces from Step 3 into the freshly churned ice cream. Pour half of this peach-cake ice cream into a 9x13 inch baking dish or similar-sized container. Drizzle with a portion of the salted caramel sauce, then add a layer of the remaining peach filling and cake pieces. Top with the remaining peach-cake ice cream, then finish with another drizzle of caramel sauce and a scattering of cake pieces for texture.
Cover the assembled dessert and freeze for at least 2 hours until solid. When ready to serve, scoop into bowls and top with extra cake pieces and a drizzle of salted caramel sauce. The contrast between the cold, creamy ice cream and the tender cake pieces makes this truly special.