How to Make It
In a skillet, melt brown sugar with 2 Tbsp. water over medium-high heat. Cook, stirring, until sugar has dissolved, about 1 minute. Stop stirring; boil until sauce has thickened and turned a dark caramel color, 2 to 3 minutes. (Mixture will bubble vigorously; do not let it burn.)
Reduce heat to low; carefully stir in peaches (mixture may spatter). Heat until peaches are just warmed through,about 1 minute. Remove from heat; stir in brandy. Transfer peach mixture to a bowl; chill at least 1 hour.
In a separate bowl, mix yogurt with sugar and vanilla; chill.
Spread a dollop of yogurt on bottom of 4 dessert bowls or wine glasses. Using a slotted spoon, top with half of peaches and some of sauce. Repeat with remaining yogurt, peaches and sauce. Cover and chill until ready to serve. Keep any remaining sauce covered and chilled. Before serving, drizzle each parfait with reserved sauce.