Make the crust: In a bowl stir together the crumbs and the sugar and stir the butter in well. Pat the mixture evenly onto the bottom and 1/2 inch up the side of a buttered 10-inch springform pan and bake the crust in the middle of a preheated 375F oven for 8 minutes. Transfer the pan to a rack and let the crust cool. In a bowl with an electric mixer, beat together the cream cheese and the sugar until the mixture is smooth; beat in the sour cream, the flour, the eggs, 1 at a time, beating well after each addition, the lime juice, the vanilla, and the food coloring, and beat the mixture until it is smooth. Pour the filling over the crust. Bake the cheesecake in the middle of a preheated 375F oven for 15 minutes, reduce the temperature to 250F, and bake the cheesecake for 50 to 55 minutes more, or until the center is barely set. (The cheesecake will continue to set as it cools.) Let the cheesecake cool on a rack and chill it, covered, overnight. Remove the cheesecake from the pan and transfer it to a cake stand. With a pastry bag fitted with a decorative tip, pipe the whipped cream into rosettes on the cheesecake. Garnish the cheesecake with the lime slices and the mint sprigs.