Preheat the oven to 250°F and liberally grease a 9x13-inch baking dish.

Cut the banana bread into 1-inch cubes (should total about 6 cups)

Place cubed banana bread and torn baguette on a baking sheet and place in the oven for 30 minutes to dry out. Depending on how moist the banana bread is, you may need to keep the banana bread cubes in the oven longer than the baguette. Set aside the dried-out banana bread and baguette pieces until needed.

To make the vanilla sauce, combine ½ cup heavy cream, ½ cup whole milk, ½ teaspoon vanilla extract, and a pinch of salt in a small saucepan. Heat the mixture over medium-high heat until it begins to simmer. Remove the saucepan from the heat and let it sit for a few minutes.

In a small bowl, whisk ¼ cup of the granulated sugar with the egg yolks. Add ¼ cup of the hot cream mixture, stirring until incorporated. Slowly add the remaining hot cream (½ cup at a time), stirring after each addition until the mixture is smooth. (Don’t worry if any clumps have formed; they will be removed through the sieve). Return the egg/cream mixture to the saucepan.

Place the saucepan over low heat, stirring constantly. Heat the mixture until it thickens slightly and takes on a velvet-like texture. It is ready when it registers 175°F on an instant-read thermometer (if you don’t have one, it is ready when it coats the back of a spoon and has thickened slightly).

Wipe clean the small bowl and place a sieve over the top. Gently pour the hot mixture through the sieve. Discard any clumps it catches. Cover the surface of the vanilla sauce with plastic wrap and set aside.

Increase the oven temperature to 350°F.

To make the banana custard, combine the remaining 1 ¼ cups heavy cream, 1 ¼ cups whole milk, mashed banana, 6 whole eggs, ½ cup of sugar, 3 teaspoons vanilla extract, and a pinch of salt. Blend on high speed for 1 minute.

Place the dried-out banana bread and baguette pieces in a large mixing bowl and pour the banana cream over the top, stirring to ensure all pieces absorb the liquid. Let the mixture sit for 30 minutes, stirring with a soft silicone spatula every 10 minutes to rehydrate the bread.

Using a silicone slotted spoon (so you don’t damage the bread), scoop the bread out of the liquid and place it into the prepared baking dish. Slowly spoon ¾ to 1 cup of the leftover banana cream over the bread (or as much as it can absorb). It is okay if there is liquid around the bread, as this will soak up during baking. You may have leftover banana cream in the bowl; don’t feel like you should use all of it, as you don’t want the bread to swim in liquid).

Bake for 30 minutes, then place a sheet of aluminum foil over the dish and continue baking for another 25-30 minutes or until the tops are golden brown and the pudding is set (when a toothpick inserted into the deepest part comes out clean).

Top with banana slices and vanilla sauce, and serve while still warm.