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While the cake bakes, prepare the cheesecake layer and set up for the water bath.
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Tear off two large sheets of heavy-duty aluminum foil. Wrap the bottom and up the sides of the springform pan to create a water-tight barrier. Place the wrapped pan into a larger roasting pan or baking dish.
 
Make the Cheesecake Layer:
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In the bowl of a stand mixer fitted with a paddle attachment (or using a hand mixer), beat the softened cream cheese on medium-low speed until completely smooth and free of lumps, about 2 minutes.
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Add the sour cream, sugar, and vanilla extract. Beat on low until combined. Scrape down the sides and bottom of the bowl.
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Add the eggs one at a time, beating on low speed just until each is incorporated. Do not overmix. If using, add the gluten-free flour and mix until just combined.
 
Assemble and Bake:
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Once the carrot cake layer is out of the oven, reduce the oven temperature to 325°F (160°C).
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Place the roasting pan with the springform pan in it into the oven. Carefully pour hot water into the roasting pan until it comes about halfway up the sides of the springform pan.
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Bake for 50-55 minutes. The edges will be set but the center will still have a slight jiggle when shaken. Do not open the oven door during baking.
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Turn off the oven. Crack the oven door open and let the cheesecake cool inside for 1 hour.
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Remove the cheesecake from the water bath and carefully remove the foil. Let it cool on a wire rack for another 30 minutes. Then, run a thin knife around the edge to loosen it from the pan (this prevents cracking as it cools).
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Refrigerate, uncovered, for at least 6 hours, or preferably overnight.
 
Make the Frosting & Serve:
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In a medium bowl, beat the softened cream cheese and butter together until smooth and creamy.
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Spread the frosting over the completely chilled cheesecake.
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Slice with a sharp knife wiped clean between cuts. Store leftovers covered in the refrigerator.
 
Top Tips:
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Room Temperature is Key: This is the most important step for a smooth, non-lumpy cheesecake.
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No Peeking: Resist opening the oven during baking to prevent the cheesecake from falling.
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Foil is Essential: Properly wrapping the pan prevents water from the bath seeping in and making the crust soggy.
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Chill Thoroughly: Patience is required! The cheesecake must be completely chilled to set properly and for clean slices.