Preheat the oven to 400F degrees. Line a large baking sheet with parchment paper or silicone baking mat. Set aside.
In a large bowl, whisk together flour, baking powder, sugar and salt. Cut in the butter, using a pastry blender or your fingers. Alternatively, you can pulse the ingredients in a food processor. Mix until mixture resembles coarse meal (uneven pieces of butter in the mixture is good!). Add 3/4 cup heavy cream and vanilla extract and stir with a spatula or a fork until dough begins to form. If dough is too crumbly, add more heavy cream - up to 1/4 cup. Don't overmix. Gently fold in bananas and chocolate chips. The dough will be slightly sticky.
Transfer dough to a floured surface and knead dough gently, about 5-6 times, until a ball forms. Pat the dough into a 9-inch (22 cm) circle, about 3/4-inch thick. Cut the circle into 8 even wedges.
Place the scones on prepared baking sheet. Brush the tops with a bit of heavy cream. Sprinkle with coarse sugar. Bake scones for 15-18 minutes, or until golden brown. Transfer baking sheet to a wire rack and allow it to cool for 10 minutes. While scones are still hot, sprinkle again with coarse sugar for extra crunchiness.
These scones are delicious either warm or at room temperature.
Scones are best eaten the same day they are made, but they can be frozen for up to 1 month.