Scrape seeds from vanilla bean into a medium bowl. Combine seeds, bean, yogurt, 1 1/2 tablespoons sugar, and a dash of salt. Let stand for 1 hour; discard bean.
Preheat oven to 350°.
Combine remaining 1/4 cup sugar, remaining dash of salt, bourbon, and vanilla extract in a large bowl, stirring with a whisk. Add peaches; toss gently. Arrange peaches, cut side down, on a parchment-lined baking sheet. Reserve sugar mixture. Bake peaches at 350° for 10 minutes. Turn peach halves over; drizzle cavities with reserved sugar mixture. Bake an additional 10 minutes or until just tender. Serve with yogurt and juices.