Line the bottom (and sides if preferred) of a 9” springform pan with parchment paper. Press the oreo crust into the bottom of the prepared pan. Chill in the fridge.
Whip the chilled heavy cream and 1/4 c of sugar in a mixing bowl until medium firm peaks form, about 5-6 minutes on medium-high speed. Scoop out into another bowl.
Add in the orange juice, greek yogurt and extract. Cream together on medium speed until smooth and well incorporated. Gently fold the whipped cream into the cream cheese mixture.
Pour the citrus cream cheese filling into the prepared crust. Smooth the filling across the pan. Cover the entire pan with plastic wrap or foil. Chill in the fridge for 12 hours - overnight.
Remove the sides of the spring form pan. Serve from the pan or carefully transfer the cheesecake to a serving plate. Right before serving, spoon the cranberry compote directly onto the cheesecake.