Bring a medium saucepan of water to a boil. Meanwhile, prepare an ice-water bath. Place peaches in boiling water for 1 to 2 minutes, remove with a slotted spoon, and transfer to ice-water bath. Remove skin, and cut peaches in half. Remove and discard pits, and slice each half into 6 wedges.
Combine sugar and 1/2 cup water in a small saucepan; cover, and cook over medium-high heat until sugar is completely dissolved, 3 to 4 minutes. Uncover, reduce heat to medium low, and cook until sugar turns medium amber, about 15 minutes. While cooking, wipe down sides of pan several times with a pastry brush dipped in cold water to prevent crystals from forming.
Working quickly, remove pan from heat, and stir in peach wedges with a wooden spoon. Return saucepan to heat, and continue cooking, stirring occasionally, until the peaches are soft, about 5 minutes.
Remove peaches and sugar syrup from heat, and let cool slightly. Transfer half the mixture to a medium bowl, and set aside. Transfer the other half to the bowl of a food processor, and puree until smooth, about 30 seconds.
Add half the puree (about 3/4 cup) to the caramelized sliced peaches. Cover with plastic wrap, and refrigerate until the cake is served. Reserve the remaining puree to assemble the cake.