In a medium saucepan, whisk together the sugar and flour until fully combined and no lumps remain. Add in the cold brew coffee and turn on the heat to medium-high. Whisk thoroughly, taking care to scrape the bottom and sides of the pot and break up any lumps. Whisk occasionally until mixture begins to bubble and thicken. Allow to bubble for about 2 minutes.
Remove from the heat and working quickly and carefully, pour a small amount of the bubbling coffee mixture into the bowl of lightly beaten egg yolks, whisking the yolk mixture constantly to prevent the eggs from scrambling. This is called tempering the eggs. Once the eggs have been incorporated with the coffee mixture, pour the egg mixture back into the coffee mixture and continue cooking in the saucepan until the mixture comes to a boil. Allow to boil for about 2 minutes, stirring constantly. Mixture will have thickened.
Remove from heat and whisk in the vanilla extract. Strain the mixture into a bowl if there are any lumps. Cool the pudding to room temperature, about 30 minutes.
Once pudding has cooled, whip the heavy whipping cream in a stand mixer with the whisk attachment until stiff peaks form, about 5-7 minutes. Fold the whipped cream (or use thawed Cool Whip here instead) gently into the pudding mixture until no streaks remain and the mixture is fully incorporated. Spread the filling into the prepared pan, then refrigerate for 6 hours, preferably overnight.
Just before serving, make fresh whipped cream to go on top: In the bowl of a stand mixer, beat the heavy whipping cream and confectioners' sugar together with the whisk attachment until stiff peaks form, about 5-7 minutes. Or, use any remaining Cool Whip you have. Spread onto the pie. Garnish with Oreo cookie crumbs, if using. Serve and store leftovers in the fridge.