Preheat oven to 350ºF and adjust rack to medium position. Oil and then line an 11×7-inch baking dish with parchment paper. Place graham crackers and whole cane sugar in the bowl of a food processor. Pulse until crackers are finely ground. Add butter and 1 1/2 tsp coffee and pulse until crumbs are moist and stick together. Reserve 1/2 cup the crumbs and set aside. Press the remaining mixture onto bottom of prepared pan. Bake for 10 minutes until golden.

Stir together the remaining coffee, 1 tablespoon cream and vanilla in a small bowl. Beat cream cheese in a large bowl until creamy. Add whole cane sugar and beat until blended. Beat in coffee mixture and egg. Spread filling evenly over crust. Bake for 20-25 minutes until set. Chill uncovered until cold and firm, at least 3 hours.

Beat remaining 1 cup cream until stiff peaks form. Serve cut bars with a dollop of whipped cream and sprinkle with crumb mixture.