In a medium saucepan, combine 2 cups of heavy cream, 1 cup of whole milk, and 1/2 cup of granulated sugar. Heat over medium heat, stirring occasionally, until the sugar dissolves and the mixture is hot but not boiling. Remove from heat and stir in 1 tablespoon of vanilla bean paste.
In a small bowl, sprinkle 2 1/2 teaspoons of unflavored gelatin over 3 tablespoons of cold water. Let it sit for about 5 minutes until it blooms. Once bloomed, add it to the warm cream mixture and stir until fully dissolved.
Pour the mixture into individual serving cups or ramekins. Allow to cool to room temperature, then cover and refrigerate for at least 4 hours, or until set.
In a separate bowl, combine the diced peaches with 1 tablespoon of lemon juice. Set aside to allow the flavors to meld.
For the rum whipped cream, in a mixing bowl, beat 1 cup of heavy cream with 2 tablespoons of powdered sugar and 1 tablespoon of dark rum until soft peaks form.
To serve, spoon the diced peaches over the set panna cotta and top with a dollop of rum whipped cream.