Pour the whole milk into a medium saucepan away from the heat and sprinkle the unflavored gelatin evenly over the surface.
Allow it to rest undisturbed for 3 to 5 minutes until the gelatin blooms. Place the pan over medium-low heat, stirring continuously until the gelatin has fully dissolved and the mixture is thoroughly warmed but not boiling, about 4 to 5 minutes.
Incorporate the heavy whipping cream, granulated sugar, vanilla extract, and a pinch of salt, maintaining a gentle stir for an additional 5 minutes until the sugar is entirely dissolved and the mixture is steaming without reaching a boil.
Remove from the heat and let stand for 5 minutes to cool slightly. Transfer the sour cream into a medium mixing bowl with a spout, then steadily whisk in the warm cream mixture until the texture is smooth and uniform.
For an extra-silky result, strain through a fine-mesh sieve if preferred. Promptly pour the mixture into six dessert glasses or eight small ramekins.
Refrigerate until the panna cotta is fully set, approximately 4 to 6 hours.
For the berry sauce, place half of the berries into a small saucepan along with the lemon juice and sugar. Bring the mixture to a gentle boil and cook for about 4 to 5 minutes until it becomes syrupy.
Stir in the remaining fresh berries and remove from the heat. Once the sauce has cooled to room temperature or is slightly warm, spoon it generously over each chilled panna cotta just before serving.