Caramelized Banana Pudding

Place rack in bottom third of oven; preheat to 450°. Line a large rimmed baking sheet with parchment paper. Sprinkle ¼ cup sugar and ½ tsp. cinnamon evenly over parchment.

Using the tip of a knife, poke holes all over 6 bananas, then cut in half lengthwise. Arrange bananas cut side down on parchment, moving them around so cut sides pick up as much cinnamon-sugar as possible.

Arrange bananas in a single layer and roast until skins are deep brown and sugar seeping from underneath bananas is deep amber, 15–20 minutes. If any liquid leaches out of the bananas, discard. Let bananas sit until cool enough to handle.

Meanwhile, whisk 3 Tbsp. cornstarch, ¼ tsp. salt, and ½ cup sugar in a medium saucepan. Very slowly stream in 2½ cups half-and-half, whisking constantly, until lump-free. Cook over medium heat, whisking constantly and vigorously, until pudding is bubbling and thick enough that wires of whisk leave a trail, 7–10 minutes.

Remove from heat. Stir in 1 Tbsp. butter and 1½ tsp. vanilla until smooth. Let cool slightly.

Scrape 4 caramelized banana halves into pot with pudding; discard skins. (Save the remaining 8 halves for layering and decorating the top.) Purée with an immersion blender or transfer to a food processor and process until smooth and creamy. Let cool while you prepare your other ingredients. The pudding should be warm but not hot when assembling (you can also make the pudding ahead of time, chill, and assemble cold).

Whisk 1½ cups sour cream and remaining 2 Tbsp. sugar and ½ tsp. cinnamon in a medium bowl until sugar is dissolved (this could take several minutes).

Remove remaining 8 bananas from their skins (you may need to use a butter knife to help scrape bananas from parchment paper).

Time to assemble: Lay 4–5 graham crackers in a single layer in an 8x8" baking dish, then spoon about one-third of sour cream mixture evenly over crackers.

Spread half of banana pudding over sour cream, then top with 3 banana halves.

Repeat with 4–5 more graham crackers, half of remaining sour cream, and all of remaining banana pudding (do not add more bananas).

Top with 4–5 more crackers, then spread remaining sour cream mixture over, working to edges of dish.

Arrange remaining 5 banana halves decoratively over.

Cover and chill pudding for at least 4 hours and up to overnight to meld the flavors.

Do Ahead: Pudding can be made 3 days ahead. Cover with plastic, pressing directly onto surface, and keep chilled.