Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Lay the peaches out on the lined baking sheet and sprinkle with 2 tablespoons of the brown sugar. Roast until lightly caramelized and tender, 25 to 30 minutes. Let cool slightly.
In a small saucepot, melt the butter over low heat. Add the honey, cinnamon, lemon juice, remaining 1 tablespoon brown sugar and a pinch of kosher salt. Add the peaches. Bring to a simmer and cook, stirring occasionally, until the liquid is slightly reduced, 3 to 4 minutes. Remove from the heat and stir in the vanilla extract. If the sauce is too thick, add 1 tablespoon of water. Serve warm over vanilla ice cream.