In a medium saucepan, whisk the sugar, cocoa powder, cornstarch and salt. Gradually whisk in the oat milk and coconut milk until smooth.Cook over medium heat, whisking constantly, until the pudding is thick and bubbling, then cook for 1 minute more. Remove from the heat and stir in the chocolate, butter and vanilla until melted and glossy.
Transfer the pudding to a bowl and press plastic wrap directly onto the surface. Let it cool at room temperature for 30 minutes, then refrigerate for 1 hour until cool.
Crush 34 of the cookies into fine crumbs in a food processor and mix with the melted butter. Press firmly into the bottom of a 9x13-inch pan and refrigerate for 15 minutes.
Beat the cream cheese, powdered sugar and vanilla until smooth and fluffy. Gently fold in 1 1/2 cups of the whipped topping, then spread evenly over the crust.
Whisk the cooled pudding until smooth and spread it evenly over the cream layer.
Spread the remaining 2 cups of whipped topping over the pudding. Coarsely crush the remaining 6 cookies and sprinkle them over the top along with the mini chocolate chips.
Cover and refrigerate for at least 4 hours or overnight until set. Cut into squares and serve cold.