TO MAKE THE CHEESECAKE:
Preheat oven to 350°F, and grease a 9-inch springform pan. Whisk crumbled Oreos and butter together in a medium bowl until combined. Press firmly onto bottom of the pan (or up the sides, if desired). Bake for 10 minutes, then remove and let cool. Reduce oven heat to 325 degrees F.
Once the pan reaches room temperature, carefully wrap the outside of the pan in 2 layers of heavy-duty aluminum foil, being sure that there are NO gaps where water could seep through. Place the pan in a large roasting dish (or any pan larger than the springform), and bring a tea kettle or pot of water to boil in preparation for the water bath. Set aside.
Using an electric mixer, beat cream cheese on medium speed for 3 minutes until smooth. Add the remaining 1 cup sugar and beat for an additional minute until well blended. Add Greek yogurt, 3/4 cup Nutella and vanilla extract, and beat for an additional minute, stopping partway to scrape the bottom of the bowl with a spatula. Add eggs, one at a time, beating on low speed after each addition just until blended. (Do not overbeat!) Pour into crust.
Place the double pans in the oven on a shelf on the bottom third of the oven. Very carefully use a tea kettle (or large measuring cup) to pour the boiling water in the larger pan to form a water bath around the springform, so that it comes up about 1-inch around the springform.
Close the oven door, and bake about 1 hour 30 min, or until center is almost set. (The cake should still jiggle ever so slightly.) Turn oven off, and open oven door slightly. Let cheesecake set in oven 1 hour. Then remove cheesecake from oven, carefully run a knife around the edges of the cake, and then let cool to room temperature. Refrigerate at least 4 hours or overnight.
Remove springform rim. If your cake is not very flat on top, you can use a knife to level it off before adding the strawberry topping if desired, or you can leave it as is. Add toppings as directed below. Then store leftover cheesecake in refrigerator in a covered container.
TO MAKE THE TOPPING:
Hull the strawberries, then quarter them lengthwise. Beginning in the center of the circle, place the strawberries in a circle pattern. Then add more in concentric rings until you reach the outside of the cheesecake.
Heat the Nutella just slightly in a microwave or double boiler until it has softened. Then use a fork or a piping bag to drizzle it across the strawberries.