Place the Oreo cookies in a food processor and pulse until they form fine crumbs. Add the melted butter and pulse again until the mixture holds together when pressed.
Transfer the crumb mixture to an 8-inch tart pan with a removable bottom. Press it evenly across the bottom and up the sides. Chill the crust in the refrigerator while you prepare the filling.
Place the chopped semi-sweet chocolate in a heatproof bowl. Heat the heavy cream in a small saucepan over medium heat until it just begins to simmer. Pour the hot cream over the chocolate and let it sit for one minute.
Stir the chocolate and cream together until smooth. Add the vanilla extract and salt, then stir once more. Pour the ganache into the chilled crust and spread it evenly.
Melt the white chocolate chips in a microwave in short bursts, stirring between each. Spoon the melted white chocolate into a small zip-top bag and snip off one corner. Pipe concentric circles over the tart surface.
Use a toothpick to drag lines from the center outward through the circles to create the web pattern. Return the tart to the refrigerator to set for at least two hours before serving.