In a large, non-reactive bowl (see baker's notes), combine 1 cup buttermilk, 1/4 cup fresh-squeezed lemon juice and the zest from 1 lemon, whisking the ingredients together until combined. Set aside.
Bloom 1 packet unflavored powdered gelatin by sprinkling it over a small bowl filled with 3 tablespoons water. The gelatin is bloomed when the gelatin granules are softened entirely, about 3 to 5 minutes — please see my baker's notes on how to bloom gelatin!
While the gelatin is blooming, combine 3 1/2 cups heavy whipping cream and 1 1/3 cups granulated sugar in a medium sauce pot. Over medium heat, warm the cream and sugar to just below a simmer, stirring continuously to dissolve the sugar.
Once the cream is just below a simmer, turn off heat and transfer the pot to a wire cooling rack. Whisk in the bloomed gelatin (from the 2nd step), whisking gently but continuously to integrate the gelatin.
Once the gelatin has been whisked into the cream, pour the hot cream into the buttermilk-lemon mixture (from the 1st step) and stir gently until the mixture looks homogenous.
Carefully transfer the mixture and pour into individual cups, transferring the cups into the refrigerator until set. Depending on our fridge, this can take as little as 3 hours, but it's best to allow the panna cotta to set overnight. Allow the panna cotta to cool down in the fridge for an hour or so, before covering each vessel with plastic wrap (in order to prevent the panna cotta from absorbing any weird flavors from the fridge).
Once the panna cotta is set, it is ready to serve. Serve cold and spoon 1 tablespoon of plum and rose water compote on top of each panna cotta serving. The panna cotta can also be enjoyed with the compote mixed in (as demonstrated by the janky gif of my boyfriend below).