Preheat the oven to 325 degrees F and assemble a 9 inch springform pan. Line it well with aluminum foil or use a baking bag to ensure water doesn’t enter.
Using a food processor, crumble the graham crackers and sugar together until finely crushed.
Add in the melted butter and pulse until the consistency of wet sand.
Press into the bottom and slightly up the sides of the pan, you can use a flat bottom cup or measuring cup to help make this easy.
Bake for 12-15 minutes or until golden brown and dry to the touch.
Allow the crust to cool while making the cheesecake.
In a large mixing bowl, beat together the cream cheese and sugar with a hand or stand mixer until smooth.
Add in the greek yogurt and vanilla extract and mix on low, just until combined.
Mix together the eggs in a small mixing bowl, without whisking, just until combined.
With the mixer on low, slowly add the eggs into the cheesecake filling, just until combined. Use a spatula to mix in everything on the sides and bottom of the bowl as well.
Once the cheesecake is made, make the chocolate swirl by placing the semi-sweet chocolate chips and heavy cream in a microwave safe bowl.
Heat for 30 seconds and then stir well. Repeat in 30 second increments until the mixture is smooth and completely melted, about 3 minutes total.
Pour half of the cheesecake mixture into the prepared crust and dollop half of the chocolate over the top.
Swirl with a knife or chopstick into your desired design.
Scoop in the remaining cheesecake filling and gently tap it several times on the counter to remove any air bubbles.
Dollop the remaining chocolate mixture on the top and then swirl the second layer of chocolate into the cheesecake with a knife or chopstick.
Place the cheesecake into a large baking or roasting pan lined with a lint free towel to keep it from slipping.
Slide the pan into the oven and then pour hot or boiling water along the outside of the springform pan until the baking or roasting pan is half filled with water. Tent aluminum foil over the top of the pan if you want to avoid a browned top.
Bake for 75-85 minutes or until the edges of the cheesecake are set and the center still wobbles slightly. The center of the cheesecake should read 150 degrees Fahrenheit with a digital thermometer.
Turn off the oven and allow the cheesecake to cool with the oven door ajar for 1 hour.
Remove the cheesecake from the water bath and cool to room temperature, about 1 hour longer.
Wrap the cheesecake well with plastic wrap and refrigerate overnight.
When ready to serve, remove the wrap and rim, slice and enjoy.