Add the cream cheese, sugar and vanilla to a stand mixer with a paddle attachment and whip on medium until it is completely smooth. Add in the peanut butter and heavy cream and mix again until smooth.
Add the eggs, one at a time, mixing and scraping down the bowl in between. Press the filling through a fine mesh strainer into a clean bowl.
Place a double layer of foil under the springform pan and mold it up the sides. Then place that foil covered pan into a baking dish. This is to allow you to create a water bath and not have water get into the crust.
Carefully pour the filling into the crust and smooth the top. Place the pan in the 325 degree oven and carefully pour hot water into the baking dish, being very careful not to get any water into the cheesecake.
Bake for 45-65 minutes (you need to go based on the temp/appearance here, not the time as it varies widely depending on your ingredient temps, oven, kitchen temp, etc). The cheesecake is done when the edges are set but the center still jiggles some when you move the pan. It should register 150 on an instant read thermometer when ready.
Carefully remove the foil lined pan from the water bath and turn off the oven. Remove the water bath and place the cheesecake pan back into the oven right away and leave the door cracked open. Let it sit in the cooling oven for 30 minutes, then move to a cooling rack on the counter to cool to room temp.