In a medium saucepan, combine diced peaches, granulated sugar, brown sugar, lemon juice, vanilla, cinnamon, and salt.
Cook over medium heat, stirring often, until the peaches release juices and start to soften, about 5 to 7 minutes.
In a small bowl, whisk cornstarch with water until smooth, then stir the slurry into the peach mixture.
Continue cooking, stirring, until the filling bubbles and thickens to a glossy, jammy consistency, 2 to 3 minutes more.
Scoop about 1/2 cup hot peach mixture into a bowl for glaze, then lightly mash it with a fork.
Let both the main filling and the small glaze bowl cool to room temperature so they do not melt the batter.