Lightly coat an 8×8 baking dish with nonstick spray. Place a layer of bread cubes evenly into the baking dish. Top with bananas and chocolate chips in an even layer, repeating 2 more times and ending with a layer of bread.
In a large glass measuring cup or another bowl, whisk together milk, eggs, butter and vanilla. Pour mixture evenly over the bread cubes. Cover and place in the refrigerator for at least 2 hours or overnight.
Preheat oven to 350 degrees F.
To make the oatmeal topping, combine oats and sugar. Add cold butter and toss to coat, using your fingers to work the butter into the dry ingredients until it resembles coarse crumbs. Sprinkle the oatmeal topping evenly over the bread cubes.
Place into oven and bake for 35-45 minutes, or until golden brown.
Serve immediately, drizzled with syrup, if desired.