Step 1 Place a rack in the upper third of the oven and heat the oven to 350 degrees. Spray a 9-inch springform pan with cooking spray and line the bottom with a round of parchment paper. Spray the parchment. Wrap the outside of the pan with aluminum foil to prevent any water from coming in from the water bath.
Step 2 Press the farmer cheese through a fine-mesh strainer to ensure the curds are fine. In the bowl of a stand mixer fitted with the paddle attachment (or use a large bowl and a hand mixer), mix the cream cheese and the sugar. Beat on low speed for 2 minutes, or until smooth, scraping down the sides of the bowl.
Step 3Add the eggs and egg yolks, one at a time, scraping down the bowl and paddle or beaters after each addition. Beat in the lemon juice and vanilla. Scrape down the bowl and paddle.
Step 4Still on low speed, beat in the sour cream. Slowly add the heavy cream, beating until blended; stop to scrape down the bowl and paddle every 30 seconds. Gently press the finished batter through a fine-mesh strainer.
Step 5Pour the mixture into the prepared pan, scraping every last bit out of the bowl with a rubber spatula. Place the pan in a baking or a roasting pan and place on the oven rack. Pour enough hot water into the baking pan to come halfway up the sides of the springform pan. Bake for 1 hour.
Step 6Turn off the oven; do not open the oven door. Leave in the oven for another 45 minutes to an hour; the cake will be golden and set (if you don't have a window, open the oven door quickly to check).
Step 7Remove the cake from the oven, remove from the water bath to a rack and cool to room temperature, about 2 hours. Chill for at least 4 hours in the refrigerator.
Step 8To serve, run a knife around the inside of the rim of the springform pan and remove the rim. Allow the cake to stand at room temperature for 20 minutes before serving.