Preheat your oven to 450 degrees F. Grease a sheet pan with cooking spray (or line it with greased parchment paper).
On a floured surface, roll out your pizza dough into an 11-inch circle. Place the circle of dough on your prepared pan and shape it as needed.
Bake the dough for five minutes without any toppings.
Meanwhile, peel your banana and slice it into rounds 1/4-inch thick.
When the dough has baked for five minutes, take it out of the oven and add your toppings. Start by distributing 1/4 cup white chocolate chips all over the dough, except for the crust border.
Add your banana slices to the pizza, again leaving a border around the edges for the crust. Sprinkle on the brown sugar.
Bake the dessert pizza for 10-14 minutes more, until the crust is browned.
Melt 1/8 cup white chocolate chips in the microwave. (Use a microwave-safe bowl and cover it loosely with wax paper.) Heat the chips for 30 seconds, stir, then heat them for 15 seconds more and stir. If needed, continue heating the chips for 15 seconds at a time until melted. Stir with a fork until smooth.
Dip your fork into the melted white chocolate, and hold the fork over the pizza to drizzle on ribbons of white chocolate.
Let the pizza rest for a few minutes, then slice into servings. Store leftovers in a sealed container in the refrigerator for up to two days.
If you wish, you can melt 1/8 cup of dark chocolate chips to drizzle on the pizza in addition to the melted white chocolate. We found using all white chocolate tasted better though.