For the peach compote, in a medium saucepan, combine peaches, light brown sugar, water, lemon zest, and lemon juice. Bring to a boil and reduce to a simmer until peaches are soften and mixture is slightly thickened, about 10 minutes. Remove from heat and stir in vanilla extract. Cool completely. Transfer to an airtight container to keep in the fridge.
For the salted caramel sauce, in a medium saucepan, add sugar and ¼ cup cold water. Stir to combine. Cook over medium-high heat until sugar has turned into a deep amber color, about 8 – 10 minutes. Do not stir. Carefully add the heavy cream, as the mixture will bubble vigorously. Reduce the heat to low, whisk until smooth, about 2 – 3 minutes. Remove from heat. Stir in the unsalted butter and salt. Set aside to cool to slightly warm.
For the icebox cake, in a large mixing bowl, whisk together mascarpone cheese, powdered sugar and vanilla until smooth. Set aside.
In a large mixing bowl with an electric mixer fitted with a whisk attachment, beat the heavy cream until soft peaks form. Add the mascarpone mixture in 2 additions, beat until just combined. Do not overmix. Transfer the bowl in the fridge to keep cool.
In the meantime, line a loaf pan (9×5-inch) with 2 pieces of plastic wraps. One lengthwise with overhang and one widthwise with overhang.
To assemble the cake, spread a thin layer of mascarpone at the bottom. Add a layer of graham crackers. Break apart some of them if needed. Add an even layer of peach compote. Fill in all the gaps. Drizzle a thin layer of salted caramel over the peaches. Add 1/3 of mascarpone and smooth the top. Add another layer of graham crackers. Then, a layer of peach compote and a layer of salted caramel. Next, spread another 1/3 of mascarpone and smooth the top. Finish the last layer with graham crackers. Fold in the plastic wrap overhang to cover up. Keep in the fridge for 8 hours or overnight.
Reserve the rest of the mascarpone in an airtight container and keep in the fridge. Transfer the caramel into another airtight container and keep in the fridge as well.
1 - 2 hours before serving, put the loaf pan in the freezer. This is not necessary, but it makes it easier to unmold, frost and slice. Unfold the plastic wrap and unmold the cake onto a serving plate and remove the plastic wrap. Frost the cake with the reserved mascarpone cream. Decorate with fresh peach slices. Reheat a couple tablespoons of salted caramel in a small bowl in microwave until just runny enough to drizzle (not too hot). Drizzle over the cake. Slice and serve.