INSTRUCTIONS

1. For the pudding, set a fine-mesh sieve over a medium-size bowl. Set aside.
2. Whisk 1/2 cup milk with yolks and cornstarch in a heatproof medium-size bowl until smooth. Combine remaining 1 3/4 cups milk with granulated sugar and vanilla seeds in a medium saucepan (reserve vanilla pod for simple syrup). Bring to a gentle simmer over medium heat. Slowly pour vanilla mixture into yolk mixture, whisking constantly, until combined. Pour mixture back into pot and return to medium heat. Cook, whisking constantly, until thick and glossy, about 1 minute. Remove from heat, then add butter and salt. Let stand for 1 minute. Whisk until fully combined. Pass through sieve to remove any lumps. Cover surface with plastic wrap and refrigerate until chilled, at least 3 hours or up to 2 days.
3. For the simple syrup, combine water, brown sugar and reserved vanilla pod in a medium saucepan. Set over medium heat and cook, stirring constantly, until sugar is dissolved, 1 to 2 minutes. Transfer to a resealable jar, cover and refrigerate, at least 3 hours or up to 2 days.
4. To assemble, whisk 1 cup cream in a large bowl until soft peaks form. Using the same whisk, mix chilled pudding in its bowl until smooth (pudding will be thick). Scrape pudding into cream and continue whisking until mixture is fully smooth and combined. Set aside.
5. Pour simple syrup into a medium-sized shallow bowl. Discard vanilla pod. Working quickly, dip both sides of half of Savoiardi biscuits into syrup mixture to fully coat, then arrange half of Savoiardi biscuits in the bottom of a 9 x 13-inch baking dish (you should have 3 rows of 6 biscuits, trimming end of biscuits in the final row to fit). Arrange half of bananas overtop. Spoon over half the pudding-mixture, using a spoon or offset spatula to spread evenly. Repeat layering by arranging remaining biscuits and bananas, then spooning over remaining pudding-mixture. Tightly cover dish with plastic wrap, then refrigerate until set, at least 4 hours or up to 2 days.
6. To serve, remove plastic wrap. Whisk remaining 1 1/4 cups cream with icing sugar in a large bowl until soft peaks form. Spoon over top, swooshing with the back a spoon. Sprinkle with coconut and garnish with more banana. Serve immediately.