Preheat the oven to 350 degrees Fahrenheit. Spray a 9x5 bread pan with nonstick spray and set it aside.
Add the dry ingredients to a large bowl; flour, baking soda, and salt, and whisk them together. Set aside.
In another bowl, add the butter and sugar and whisk them together for a couple of minutes.
Add the mashed bananas, eggs, and vanilla extract and mix them into the butter mixture until just combined.
Add the dry ingredients into the wet ingredients, and gently stir them together until they are combined.
Toss the raspberries and white chocolate chips in 1 Tablespoon of flour.
Add the raspberries and white chocolate chips and gently fold them into the batter.
Spoon the batter into the prepared baking pan, and sprinkle the top with a couple extra white chocolate chips, and raspberries.
Sprinkle the top with coarse sugar.
Bake in the preheated oven for 60 to 65 minutes, or until a toothpick inserted in the center of the loaf comes out clean.
Remove from oven and let the loaf cool on the rack for 10 minutes, then go around the edges of the pan with a butter knife. Turn the loaf pan over and place the bread on a cooling rack to cool completely.