Place peach halves onto a kitchen sheet pan with skin side down. Sprinkle each half of peach with brown sugar. Roast until peach halves have browned, about 3-5 minutes. Remove from oven and allow to cool slightly.
Make Pistachio Crumble Topping:
Preheat oven to 350º F.
Cut butter into flour and brown sugar with a pastry blender or two forks in a medium bowl. Stir in oats, pistachios and salt. Spread onto a small kitchen sheet pan and toast, about 10 minutes. Remove from oven and allow to cool.
Assemble Peach Parfaits:
Place one roasted peach half in the bottom of a parfait dish or glass. Top with about 1/4 cup greek yogurt. Drizzle with honey and sprinkle crumble topping on top.