Preheat oven to 325 degrees F. 

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Bring Champagne or sparkling wine to a boil in a small saucepan over medium high heat. Reduce heat to a simmer and continue to cook until liquid is reduced to 1/4 cup, approximately 8 minutes. Remove from heat and allow to cool. 

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In a separate bowl, combine cracker crumbs, 1/2 cup sugar, and butter. Press onto the bottom and up the sides of a greased 9-inch spring-form pan. Spread sliced strawberries over the bottom. 

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In a large mixing bowl, beat cream cheese and remaining sugar until smooth. Add condensed milk, cornstarch, and Champagne. Add eggs and egg yolks. Beat on low until combined. Pour over strawberries. 

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Wrap the outside of the spring-form pan in aluminum foil. Place pan on a baking sheet with sides or in a roasting pan. Place the pan on the center rack of the oven. Fill the outer pan with about 1/2-inch of hot water. Close the oven and bake for 1 hour and 15 minutes to 1 hour and 20 minutes, or until center is set. 

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Turn off the oven, but do not remove the cheesecake. Crack the oven door and allow the cheesecake to cool in the warm oven for 1 hour. Afterwards, remove the cheesecake, carefully run a knife around the edge of the pan, cover, and place in the fridge overnight. 

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Remove sides of the spring-form pan. Slice remaining strawberries and arrange them over top of the cheesecake. 

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In a microwave or double boiler, melt white chocolate chips and 1/2 teaspoon shortening. Stir until smooth and then drizzle over strawberries. Repeat melting and drizzling with milk chocolate chips and remaining shortening.