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.