In the bowl of the stand mixer, place the softened cream cheese. Beat on medium speed to combine and break up the cream cheese.
Scrape the sides and bottom of the bowl, then beat for another minute.
Scrape the sides and bottom of the bowl again, then add in the sugar and salt. Beat until combined.
Scape the bowl again, then beat for an additional minute, ensuring everything is well blended.
Add in the cream, lemon juice and vanilla. Beat on low until combined, about a minute.
Scrape the bowl. Add both egg yolks and mix until combined, about a minute.
Scrape the bowl. Add in the eggs, 1-2 at a time, beating until combined, scraping the bowl between additions.
Lightly brush the sides of the springform pan with melted butter.
Place the springform into a roasting pan or a large (14") cake pan. Prepare a pitcher of hot water.
Pour the cheesecake mixture into the pan, and use an offset spatula to smooth out the batter.
Place the roasting pan into the oven. Fill the roasting pan with the hot water, just enough to come halfway up the sides of the foil of the springform pan.
Bake the cheesecake until the cheesecake jiggles slightly, no longer appears wet and an instant read thermometer reads 150F, about 60-90 minutes.
Once done baking, turn off the oven. Prop the oven door open slightly with a wooden spoon. Let the cheesecake slowly cool in the water bath in the oven for 45 minutes.
Remove the cheesecake from the oven. Remove the foil. Place the cheesecake on a wire rack.
Run a small knife around the edge of the pan to loosen the cheesecake and keep it from splitting in the middle.
Cool the cheesecake to room temperature, about 2-3 hours.
Wrap the top of the pan with plastic wrap, and refrigerate for at least 3 hours.