Panna cotta is an Italian dessert whose name means "cooked cream," which aptly described this simple yet fancy make-ahead treat. The creamy individual puddings get a festive finish with a topping of sweet-tart balsamic raspberries.
Sprinkle gelatin over 1/4 cup milk in a small bowl. Let stand until gelatin softens, about 5 minutes.
Place a fine mesh sieve over a heatproof bowl near the stove. Whisk egg yolks and sugar in a second heatproof bowl until combined. Heat cream and remaining 3/4 cup milk in a medium saucepan over medium heat, stirring often, until simmering. Gradually whisk hot cream mixture into egg mixture. Return mixture to saucepan. Cook over low heat, stirring constantly with a wooden spoon, until mixture coats spoon (a finger run through the custard on the spoon will cut a swath) and an instant-read thermometer reads 185ºF, about 3 minutes. Pour through the sieve into bowl. Discard any bits of cooked egg white in the sieve. Add the gelatin-milk mixture and rum extract to cream mixture and whisk until gelatin is completely dissolved, about 1 minute. Let stand 5 minutes to cool slightly.
Divide cream mixture evenly among ramekins. Cover each with plastic wrap. Refrigerate until chilled and set, at least 2 hours.
Whisk brown sugar and balsamic vinegar together in a medium bowl to dissolve sugar. Stir in raspberries. Let stand at room temperature for at least 15 minutes and up to 2 hours.
To unmold each panna cotta, run a dinner knife around inside of ramekin to release panna cotta. Hold a dessert plate firmly over ramekin and invert plate and ramekin together. Shake firmly to unmold panna cotta onto plate. Top each panna cotta with an equal amount of raspberries and their juices. Serve immediately.