To prepare panna cotta: Place 1/4 cup hot coffee in a small heatproof glass bowl. Sprinkle gelatin over the coffee; stir to mix. Let stand for 5 minutes.

Meanwhile, whisk the remaining 3/4 cup coffee, yogurt, milk, 2 teaspoons brandy, vanilla and cinnamon in a medium bowl.

Microwave the coffee-gelatin mixture, uncovered, on High until the gelatin has completely dissolved but the liquid is not boiling, 20 to 40 seconds. (Alternatively, set the bowl in a small skillet of simmering water until the gelatin has dissolved completely.) Stir until smooth. Add granulated sugar and stir until dissolved.

Slowly whisk the gelatin mixture into the yogurt mixture. Refrigerate, stirring occasionally, until it just begins to thicken, 30 to 45 minutes.

Beat the cream with a whisk or electric mixer until soft peaks form. Whisk into the yogurt mixture until smooth. Divide among six 4-ounce (1/2-cup) custard cups. Cover and refrigerate until the panna cotta is chilled and set, at least 4 hours and up to 3 days.

To prepare sauce: Combine brown sugar and 3 tablespoons coffee in a small skillet. Bring to a boil over medium-high heat, stirring frequently, until the liquid is reduced by half, about 2 minutes. Remove from the heat and pour in 2 tablespoons brandy. Tilting the pan away from you, use a long-handled match (or grill lighter) to carefully ignite the liquid, gently shaking the pan until the flames subside. Let cool slightly.

To serve: Run a knife around the cups to loosen the panna cotta. One at a time, set the cups in hot water for 30 to 40 seconds, then invert onto a serving plate, holding the cup and plate tightly together. If it doesn't unmold, carefully run the knife around the edge of the cup to loosen the panna cotta again, then invert onto the plate. Drizzle each panna cotta with a little of the sauce.