Lower the oven temperature to 325 degrees F.
Place the cream cheese and sugar in bowl of a stand mixer. Beat on medium speed with paddle attachment until smooth and well combined.
Add in the heavy cream, créme frâiche, yuzu juice, vanilla, and salt and beat on low speed until combined.
Add in the eggs, one at a time, and beat just until combined.
Sift the cornstarch over the batter and beat until combined.
Pour the batter into the pan with the cooled crust. Spread out evenly with a spatula as needed. Tap the pan a few times on the counter to get rid of any air bubbles.
Bring a medium saucepan of water (about 2 quarts) to a boil on the stove.
Wrap the springform pan in two layers of aluminum foil, making sure the foil comes up the sides of the pan. This is to prevent any water from the water bath from leaking into the pan.
Place the pan in a large roasting pan that can fit the the springform pan. Place the pan on the lower oven rack.
Pour the boiling water into the roasting pan, filling it up about halfway up the springform pan.
Bake cheesecake for 65-75 minutes, until the center is just set and still jiggles slightly.
Turn off the oven, crack the door open about an inch and let the cheesecake cool inside the oven for an hour.
Remove the cheesecake from the oven and the water bath, and let cool on a wire rack for another hour.
Place foil over the top of the springform pan (not touching the cheesecake) and chill in the refrigerator for at least 4 hours, or overnight.
Spread a layer of yuzu curd over the top of the chilled cheesecake. Refrigerate for an hour or so to let it set before serving.