Directions

Prepare an 8-inch springform pan with 3-inch high sides (or use a 9-inch pan for a thinner cheesecake). Rub the inside of the pan lightly with room-temperature butter. Place 2 crisscrossed pieces of parchment paper inside the pan and press the sides as smooth as possible. You should have about 2 inches of parchment sticking up on all sides.  
In the bowl of a stand mixer fitted with the paddle attachment, combine the cream and cheese and goat cheese. Beat on medium speed until smooth. Scrape down the sides of the pan and add ¾ cup sugar, flour, lemon zest, and salt. Beat on medium speed until smooth, 1-2 minutes. 
Crack the eggs into a measuring pitcher and add the egg yolks. Scrape down the mixer and paddle again, and with the mixer running on medium-low, add in the eggs one at a time, beating until smooth after each egg and scraping the bowl and paddle every couple of eggs.  
With the mixer still on medium-low, gradually pour in the cream and vanilla. Scrape the mixer once more, and beat until the mixture is smooth. It should be the consistency of thick heavy cream.  
Pour the cheesecake batter into the prepared pan and set the pan on a rimmed 9x12-inch baking sheet. Swirl a knife through the batter several times to pop any large bubbles. 
Refrigerate the cheesecake in the pan for 1-2 hours. This will help keep the center gooey while the outside browns.  
To bake the cheesecake, position a rack in the center of the oven and preheat to 450ºF. Bake the cheesecake for 20 minutes. The top should be just starting to puff and turn golden at this point.  
Increase the oven temperature to 500ºF and continue baking for 10-20 more minutes. The cheesecake is done when it’s puffed and deeply golden on top, the center wobbles like Jell-O when you give it a gentle shake, and the internal temperature measures 170-175ºF with an instant-read thermometer inserted 2 inches into the cheesecake.  
Place the baked cheesecake on a wire rack to cool to room temperature, at least 2 hours and up to 4 hours.  
Release the sides of the springform pan and use the parchment to drag the cheesecake onto a serving platter. Use a sharp knife to cut the cheesecake into wedges and serve at room temperature.  
The cheesecake keeps well, covered and refrigerated, for up to 5 days. Bring slices to room temperature before serving for the best texture and flavor.