Set to 400°F. Line a baking sheet with parchment paper.
Peel and slice the peaches. Toss them in a bowl with brown sugar, granulated sugar, lemon juice, cinnamon, salt, and optional bourbon or vanilla if using.
Spread the peaches evenly on the prepared baking sheet. Roast for 18 to 22 minutes, until soft, jammy, and caramelized at the edges.
Let the peaches cool slightly, then blend until completely smooth. Chill before using.