Adjust the oven rack to the middle position and preheat the oven to 350°F (177°C). Place a bowl of water on the lower rack. The steam will help the cheesecake to bake evenly and will keep it from splitting or cracking.
Using a hand-held or stand mixer fitted with a paddle attachment, beat the cream cheese and granulated sugar on medium speed until the mixture is smooth and creamy, 1-2 minutes.
Add the sour cream, flour, orange juice, and zest. Mix until combined.
Whisk eggs and pour into the mixing bowl, beat until combined. Whisk eggs and pour into the mixing bowl, beat until combined. Avoid over mixing to keep the cheesecake from deflating and cracking.
Remove the plastic lid from the pie crust and set it aside until needed. Pour the batter into the crust. Tap gently on the counter to bring any bubbles to the surface. Add approximately 5 tablespoons of mulberry preserves to the surface of the cheesecake. Swirl the preserves into the cheesecake using a chopstick or butter knife.
Bake the cheesecake in the center rack for approximately one hour, or until the center is almost set but slightly jiggly. If the cheesecake begins to brown on top too quickly, gently tent it with foil for the remainder of the baking time.
Turn off the oven and leave the door slightly ajar. Let the cheesecake cool down in the oven for an hour. Cool cheesecake on the counter for another hour, then chill in the refrigerator for 4 or more hours.
Pour the remaining mulberry preserves over the cooled cheesecake and spread evenly to cover the entire surface. Cover with the plastic lid and crimp the edges to keep the lid on.