Preheat oven to 375°. Line a rimmed baking sheet with parchment paper.
In a large bowl, whisk together flours, caster sugar, baking powder, and salt. Using a pastry blender or 2 forks, cut in cold butter until it resembles coarse crumbs. Add toffee bits, stirring well.
In a small bowl, whisk together banana, 1 egg, and 1 tablespoon buttermilk. Add banana mixture to flour mixture, and stir until a crumbly dough begins to form.
Turn out dough onto a lightly floured surface, and knead until a smooth dough forms. Using a rolling pin, roll out dough to a ½-inch thickness. Using a 2¼-inch round cutter, cut 12 scones from dough, rerolling scraps as necessary. Place on prepared baking sheet. Freeze for 10 minutes.
In a small bowl, whisk together remaining 1 egg and remaining 1 tablespoon buttermilk. Brush tops of scones with egg wash.
Bake until scones are golden brown and a wooden pick inserted in centers comes out clean, approximately 14 minutes. Serve warm.
Recipe by TeaTime Magazine at https://teatimemagazine.com/banoffee-scones/