Step 1

Preheat oven to 350°F. Pulse crackers in a food processor until finely ground, 6 to 8 times. Add egg white, butter, and 3 tablespoons of the sugar. Pulse until well combined, about 4 times.

Step 2

Scatter crumb mixture evenly on bottom of a 9- or 10-inch tart pan with removable bottom. Using a straight-sided glass or dry measuring cup, firmly press crumbs on bottom and against sides of pan.

Step 3

Bake crust in preheated oven until golden brown around the edges, 12 to 14 minutes. Cool completely on a wire rack, about 30 minutes.

Step 4

Meanwhile, pour cream into a small saucepan. Using a small knife, split the vanilla bean lengthwise. Using back of knife, scrape seeds from bean into cream; discard pod. Sprinkle gelatin evenly over cream. Let stand 5 minutes. Stir in remaining ½ cup sugar. Cook over medium-low, stirring constantly, until gelatin and sugar are dissolved, 4 to 5 minutes.

Step 5

Transfer cream mixture to food processor. Pinch cream cheese into 1- to 2-inch pieces, and place in food processor. Add buttermilk and salt. Process mixture until smooth, 20 to 30 seconds; pour into cooled tart crust. Chill until set, 8 hours or up to 1 day. Before serving, scatter berries over top; garnish with basil leaves.