Using an electric mixer, beat butter until creamy. Gradually add sugar, beating well. Add eggs, one at a time, stopping halfway to scrape down sides of the bowl.
In a small bowl, stir together bananas, 1/4 cup heavy cream, vanilla extract, lemon juice, and almond extract.
In another bowl, combine flour, baking powder, baking soda, salt, and cinnamon.
With mixer on low, add half of flour mixture to mixing bowl. Add all of banana mixture and then remaining flour mixture. Beat just until evenly combined. Stir in white chocolate morsels.
Bake for 50 to 60 minutes, or until a wooden pick inserted in the center comes out clean. Cool in pans for 10 minutes and then remove to wire rack to cool completely.
Make custard. Whisk eggs, vanilla extract, cinnamon, nutmeg, and half-and-half in a medium bowl. Cut one loaf of banana bread into 9 slices.
Heat a griddle or large nonstick pan over medium-high heat.
Add three slices of bread to custard, flip them over after 30 seconds to coat the other side.
Melt 1 tablespoon of butter in pan and add the 3 slices of custard-coated bread. Cook until lightly browned on both sides, about 2 minutes per side. Repeat 2 more times with remaining bread slices.