Preheat the oven to 350 degrees F. Using large pieces of heavy-duty aluminum foil, wrap the bottom and sides of a 9-inch springform pan two or three times to ensure that it's water proof as you will be baking the cheesecake in a water bath; set aside.
Place the cookies in a food processor and process the cookies until they're finely ground (about 30 seconds).
Add the butter and pulse 10 to 15 times.
Dump the cookie crumbs into the springform pan and using your hands, spread the cookie crumbs in an even layer across the bottom of the pan only (not up the sides). Place the prepared crust in the refrigerator while you prepare the filling.
Place the cream cheese in a food processor or mixer and mix until smooth. Add the sugar and mix well.
Add the eggs and the egg yolks one at a time and mix well after each addition.
Add the lime juice and mix well.
Pour the cheesecake batter into the prepared pan. It will be liquidy.
Place the cheesecake inside a large, shallow roasting pan. Pour hot water inside the pan until it reaches half-way up the sides of the springform pan with the cheesecake. Carefully put the cheesecake in the oven. Bake the cheesecake for 50 minutes and then check it. The cheesecake is done when it's set, but not firmly set so that it's still jiggly in the middle (the cheesecake will set further as it cools).
Remove the cheesecake from the oven and immediately remove it from the water bath. Carefully peel off the aluminum foil and set the cheesecake to cool on a wire rack.
Once cooled, place the cheesecake in the refrigerator until ready to serve.