Combine raspberries, 1/3 cup sugar, 1 tablespoon lemon juice, water, and balsamic vinegar in a saucepan over medium heat. Bring to a simmer and cook until sugar dissolves and berries collapse, 2 to 3 minutes. Remove from heat and strain into a bowl. Cool to room temperature, cover and refrigerate until thoroughly chilled.

Combine 2 cups sugar, 2 cups water, 2 tablespoons lemon juice, and split vanilla bean in a large saucepan and bring to a simmer over medium heat.

Place peach halves with cut sides up in the syrup and simmer until tender, 5 to 8 minutes per side, basting with the syrup occasionally. Remove from heat and allow to cool in the syrup. Transfer to a bowl, cover, and refrigerate until thoroughly chilled, about 4 hours.

Remove peach skins and serve each peach half on top of a scoop of ice cream in a bowl. Spoon the raspberry sauce over the top. Garnish with toasted, slivered almonds.