For the crust, stir together graham cracker crumbs, 3 tablespoons sugar and melted butter until completely combined. Press mixture into a 9-inch tart pan with removable bottom and place on a rimmed baking sheet; bake until crust is fragrant and golden brown, 10 to 12 minutes; remove from oven and let cool.
For the filling, combine cream cheese, lemon juice and 2/3 cups sugar in a mixing bowl and beat until smooth. In a separate bowl, whip cream and vanilla to soft peaks, then gently stir into cream cheese mixture until completely combined. Transfer filling into cooled crust, loosely cover and chill 3 hours or up to a day.
To serve, remove the tart ring and slide a spatula under tart to release it from the pan base. Transfer tart to a serving platter and scatter berries on top. Brush berries with heated honey, if desired.