For the lemon curd: Combine the granulated sugar, butter, lemon zest and juice and egg in a large microwave-safe bowl (the mixture will bubble and triple in volume during cooking). Microwave on high in 1-minute intervals, stopping to remove the bowl and stir well after each interval. Continue until the curd thickens enough to coat the back of a spoon, about 6 minutes. Strain into a clean bowl, cover the surface with plastic wrap and cool in the refrigerator (the curd will continue to thicken as it cools).
For the lemon cheesecake layer: Combine the cream cheese, cream, confectioner's sugar, lemon zest and juice and extract in a large bowl and beat with an electric mixer until it holds stiff peaks. If the cream cheese isn't very soft, you may have to whip for up to 5 minutes to get the lumps out. Refrigerate until ready to use.
For the parfait: Divide half of the cake among six 2-cup mason jars or glasses (1/2 cup of cake per jar). Top with about half of the cream cheese mixture (about 1/4 cup) followed by all of the lemon curd. Divide the remaining cake, followed by the cream cheese mixture, among the jars. Top with the blackberries. Eat immediately or refrigerate up to 4 hours.