In a medium saucepan add the champagne and cornstarch over medium heat. Cook for 10-15 minutes until reduced by hand to ½ cup. Do not boil. Set aside to cool
In a large mixing bowl, beat the cream cheese until smooth. Add sugar and continue to beat until well combined.
Add eggs one at a time, beating well after each addition. Stir in heavy cream, champagne, and vanilla extract until the batter is smooth.
Pour the batter over the prepared crust and smooth the top with a spatula.
Using a piping bag or a spoon disperse the strawberry mixture in different spots around the cheesecake. Use a knife or a skewer to create a swirl pattern on the cheesecake.
Place the springform pan in a roasting pan. Pour boiling water into a large roasting pan until it comes about halfway up the sides of the springform pan.
Bake in the preheated oven for about 55-60 minutes or until the center is set.
Once the cheesecake is done, let it cool in the pan for about 15 minutes, then run a knife around the edge to loosen it. Allow it to cool completely in the refrigerator.
Chill the cheesecake for a few more hours or overnight before serving.