Line the bottom of a 9" springform pan with parchment paper and secure the bottom.
Turn your cookies into fine crumbs in the food processor or by smashing in plastic freezer bag.
Combine crumbs with melted butter in medium sized bowl and then flatten on the bottom and up the sides of the springform pan. Set aside.
To make the cheesecake filling:
In a stand mixer bowl, beat cream cheese on medium high speed with the paddle attachment until completely smooth and fluffy, scraping occasionally, about 3 minutes.
Add the sugars and 1/4 cup of the cookie butter to the cream cheese. Cream mixture until well combined. Scrape again.
In a separate bowl mix cornstarch, salt, vanilla extract, heavy cream and lemon juice. Stir very well to get any and all cornstarch lumps out. Combine well with the cream cheese mixture.
Add whole eggs one at a time. Mix until combined. Scrape again.
Pour cheesecake batter onto crust in springform pan. Allow at least 1/2" of room at the top for the cheesecake to expand while cooking, so you may end up with a bit of excess batter.
Heat 3/4 cup cookie butter just until melted, about 40 seconds in the microwave. Pour onto filling and use a knife to swirl.
To bake the cheesecake:
Preheat oven to 350 degrees F.
You may want to line the bottom rack with foil just in case any butter from the crust seeps out while baking to keep your oven clean.
Bake at 350 degrees F for 10 minutes. Reduce heat to 275 degrees F and bake and additional 70-80 minutes until center jiggles but edges are set. Turn oven heat off, crack oven door, and allow cheesecake to finish cooking in turned off oven.
Chill overnight before removing from springform pan.