2 quarts strawberries (about 2 lbs), washed, dried and stemmed
14 oz blackberries, washed and dried
1/2 cup plus 5 tbl sugar
2 tsp unflavored powdered gelatin
1 cup heavy cream
1/4 cup sour cream
3/4 tsp vanilla extract
2 graham crackers, finely crushed
fresh mint leaves (optional)
Process 1 quart strawberries, 1/2 of the blackberries, and 1/2 cup sugar in food processor until mixture is completely smooth, about 1 minute. Strain berry puree through fine-mesh strainer into 4-cup liquid measuring cup (you should have 2 1/2 cups puree; reserve any excess for another use). Transfer 1/2 cup puree to small bowl and sprinkle gelatin over top; stir until gelatin is incorporated and let stand at least 5 minutes. Heat remaining 2 cups puree in small saucepan over medium heat until it begins to bubble, 4 to 6 minutes. Remove pan from heat and stir in gelatin mixture until dissolved. Transfer gelatin-puree mixture to medium bowl, cover with plastic wrap, and refrigerate until cold, about 2 hours.
Meanwhile, chop remaining 1 quart strawberries into rough 1/4-inch pieces. Toss strawberries, remaining blackberries, and 3 tablespoons sugar together in medium bowl. Cover with plastic wrap and set aside for 1 hour.
Place cream, sour cream, vanilla, and remaining 2 tablespoons sugar in chilled bowl of stand mixer. Beat on low speed until bubbles form, about 30 seconds. Increase speed to medium and continue beating until beaters leave trail, about 30 seconds. Increase speed to high; continue beating until mixture has nearly doubled in volume and holds stiff peaks, about 30 seconds. Transfer 1/3 cup whipped-cream mixture to small bowl and set aside.
Remove thickened berry puree from refrigerator and whisk until smooth. With mixer running at medium speed, slowly add two-thirds of puree to whipped-cream mixture; mix until incorporated, about 15 seconds. Using spatula, gently fold in remaining thickened puree, leaving streaks of puree.
Transfer uncooked berries to fine-mesh strainer; shake gently to remove any excess juice. Divide two-thirds of berries evenly among 6 tall parfait or sundae glasses. Divide creamy berry mixture evenly among glasses, followed by remaining uncooked berries. Top each glass with reserved plain whipped-cream mixture. Sprinkle with crushed crackers and garnish with mint sprigs, if using. Serve immediately.