Combine the fresh blackberries, granulated sugar, ground ginger, and lemon juice in a medium saucepan set over medium heat.

Cook the mixture for 8 to 10 minutes, stirring occasionally, until the blackberries break down, release their juices, and form a slightly thickened syrup.

Remove the saucepan from the heat and use a fork to gently mash about half of the blackberries for a varied texture, then let the mixture cool completely before chilling in the refrigerator for 15 minutes.

In a large chilled mixing bowl, combine the heavy whipping cream, vanilla extract, and powdered sugar, then beat with a hand mixer on medium-high speed for 2 to 3 minutes until stiff peaks form.

Gently fold three-quarters of the chilled blackberry mixture into the whipped cream using a rubber spatula, leaving beautiful, distinct purple streaks rather than fully incorporating the fruit.

Spoon the streaked mixture into four serving glasses, drizzle the remaining blackberry sauce over the top, and garnish with the crushed ginger snap cookies for a satisfying crunch just before serving.