Preheat the oven to 350°F (177°C). Line 8in (20cm) square baking pan with a foil, leaving 2 sides hanging over the edges.
In a food processor, pulse Oreo cookies until fine crumbs. In a medium bowl, mix the cookie crumbs with melted butter. Press the crumb mixture in the bottom of prepared baking pan. Set aside.
In a mixing bowl with whisk attachment beat the cream cheese, Greek yogurt and sugar until smooth and creamy, about 2 minutes. Add the egg, flour, vanilla extract and salt. Mix until just combined, about a minute.
In separate bowls, melt the dark and white chocolates until smooth, using a double boiler or microwave, or both (*See the notes below).
Pour about 2/3 of the cream cheese mixture into melted dark chocolate. And mix the remaining cream cheese mixture into melted white chocolate. Using a spatula, mix both mixtures until smooth.
Spoon both mixtures in an alternating pattern into the cookie crust in the baking pan. Swirl the two mixtures with a toothpick, or skewer. Tap on the counter a few times to release the bubbles. Bake the cheesecake until it’s set on the edges and slightly wobbly in the center, for about 23-25 minutes. Cool the cheesecake to room temperature, then refrigerate for at least 2 hours. Cut into 16 squares, before serving.
Notes
To melt both chocolates simultaneously, I melted white chocolate in the microwave according to the directions on the packaging (Microwave for 30 seconds at high and stir. Then another 3o sec and stir. If needed, microwave for additional 10 sec until it’s nice and smooth.) I recommend to finely chop the white chocolate before microwaving, it helps to melt better and faster that way.As for the dark chocolate, I placed the chocolate pieces in a heatproof bowl and melted the chocolate over simmering water, aka double boiler.