Preheat the oven to 350 degrees F.
To make the crust: Using a food processor, pulse the shortbread cookies into crumbs. Pour into a medium bowl and stir in sugar and melted butter until well combined. Mix the shortbread cookies and melted butter until well combined. Pour into a 9-inch spring-form pan. Press the crumbs into the bottom of the pan and about 1-inch up the sides. Bake for 8 minutes. Take the pan out of the oven and cool to room temperature.
Raise the oven temperature to 450 degrees F.
To make the filling: Using a handheld or stand mixer fitted with a paddle attachment, cream the cream cheese and sugar in a bowl on medium-high speed until light and fluffy, about 5 minutes. Reduce the speed of the mixer to medium and add the eggs and egg yolks, one at a time, mixing well. With the mixer on low, add the greek yogurt, lemon essential oil and vanilla. Mix thoroughly and pour into the cooled crust. Bake for 15 minutes. Turn the oven temperature down to 225 degrees F and bake for another 1 hour and 15 minutes. (see RECIPE NOTES) Turn the oven off and open the door wide. The cheesecake WILL NOT be completely set in the center. Allow the cheesecake to sit in the oven with the door open for about 30 to 40 minutes. Take the cheesecake out of the oven and allow it to sit at room temperature for another 2 to 3 hours, until completely cooled. Wrap and refrigerate overnight. Remove the cheesecake from the spring-form pan by carefully running a hot knife around the outside of the cheesecake. Serve with raspberry champagne sauce. Yummy!