Have ready a fine-mesh sieve over a medium bowl. In a medium saucepan, off heat, whisk together sugar, cornstarch, and salt. Very gradually (a few tablespoons at a time), whisk in milk, taking care to dissolve cornstarch; whisk in egg yolks.
Whisking constantly, cook mixture over medium heat until the first large bubble forms and sputters. Reduce heat to low; whisking constantly, cook 1 minute. Remove from heat, and immediately pour through sieve into bowl. Stir butter and vanilla into hot pudding. Let pudding cool slightly; meanwhile, slice bananas.
In six 8-ounce glasses, alternately layer warm pudding with cookies and bananas, ending with pudding and covering bananas as completely as you can to prevent discoloration. Refrigerate until set, at least 1 hour, and covered with plastic wrap, up to 2 days.
To serve, top with whipped cream and more crumbled cookies and sliced bananas.