Divide the strawberries among six cups of glasses that hold at least 6 ounces each. Chill the glasses.
Pour 1/2 cup of the buttermilk into a 2-quart saucepan and sprinkle the gelatin over the top. Set aside for 5 minutes to allow the gelatin to soften. Warm gently over medium heat and stir the sugar in. Heat gently until the gelatin and sugar have both fully dissolved, then turn off the heat.
Whisk in the remaining buttermilk and the cream, vanilla, pepper, and salt. Taste to check sweetness; add more sugar if desired.
Transfer the mixture to a measuring cup with a spout. Divide this mixture among the child cups, pouring it over the strawberries. Cover the glasses lightly with plastic wrap. Refrigerate the panna cotta and let it set for at least 2 hours--but preferably overnight. The panna cotta can be made up to 3 days ahead and left in the refrigerator, covered.