With an electric mixer, beat the cream cheese until it is soft and fluffy, about 2 minutes. Mix the flour with the remaining sugar and add it and half the maple syrup to the cheese in thirds, mixing after each addition. Add the eggs and the yolks to the batter one by one, beating after each addition. Add the heavy cream and mix again. Pour the batter into the crust and bake for 15 minutes. Lower the oven to 200 degrees and bake for an hour more. Turn off the oven, leave the door halfway open and let the cheesecake cool in the oven for a half-hour. Chill in the refrigerator for 4 hours and not more than 24.