Place six small heat-safe dessert glasses, ramekins, or molds on a tray that will fit in the refrigerator.

Sprinkle the gelatin evenly over the cold water in a small bowl. Let it stand for 5 minutes so the gelatin absorbs the water and becomes soft.

Combine the heavy cream, milk, sugar, vanilla, and salt in a medium saucepan. Warm over medium-low heat, stirring often, until the sugar dissolves and the mixture is hot and steaming. Do not let it boil.

Remove the saucepan from the heat. Add the softened gelatin and whisk until it has completely dissolved and the mixture is smooth.

Divide the panna cotta mixture among the prepared glasses or molds. Let them cool at room temperature for about 15 minutes, then cover and refrigerate until fully set, at least 4 hours or overnight.

For the berry sauce, combine the berries, sugar, and lemon juice in a small saucepan. Cook over medium heat, stirring gently, until the berries release their juices and the sauce is lightly thickened, about 5 to 7 minutes. For a smoother sauce, mash some of the berries with the back of a spoon.

Cool the berry sauce completely, then refrigerate until needed.

Serve the chilled panna cotta in glasses, or briefly dip the bottoms of unmolded ramekins in warm water and invert onto small plates. Spoon the cold berry sauce over each portion just before serving.