Heat oven to 325°. Combine shortbread rounds and 1/2 cup coconut in a food processor until small crumbs form. Add butter and pulse until combined. Using a measuring cup, press into bottom and halfway up sides of a 9-inch springform pan. Place on a rimmed baking sheet.Advertisement
In a large bowl, whisk sugar, cornstarch and salt until blended. With a hand mixer, beat in cream cheese for 2 minutes. Beat in eggs one at a time on low, then beat in cream of coconut, heavy cream and vanilla just until smooth. Pour into pan over crust.
Fill a 13-x-9-inch baking dish halfway with warm water; place on bottom oven rack. Place cake on middle rack and bake 1 hour and 10 minutes, until set (cake will still be a bit jiggly in center). Turn off oven and keep cake inside for 30 minutes, with the oven door slightly ajar. Transfer to a rack on the counter to cool completely. Refrigerate overnight.
Bring jam to a simmer in a small saucepan. Stir in strawberries. Remove from heat and cool 15 minutes. Remove cheesecake from refrigerator. Carefully run a knife along edges of cake to loosen, then release from springform pan. Pour strawberry glaze on top, allowing some to drip down sides. Refrigerate 1 hour. Sprinkle with 1/4 cup coconut just before serving.