Preheat the oven to 375 degrees F. Line a large rimmed baking sheet with parchment paper.
In a medium bowl, whisk together the mashed bananas, milk and vanilla. Set aside.
In a large bowl, whisk together the flour, sugar, baking powder and salt. Working over the bowl, grate the cold butter on the large holes of a box grater. Gently toss the grated butter in the flour until it resembles coarse meal. Stir in the wet ingredients just until evenly moistened.
Transfer the dough to a lightly floured surface, gather any crumbs and knead a few times until the dough just comes together. Working quickly and using lightly floured hands, pat the dough into a 9-by-6-inch rectangle. Using a large knife, cut the dough into 8 rectangle scones. Transfer the scones to the prepared baking sheet and brush lightly with milk; freeze for 5 minutes if the dough is too warm. Arrange the banana slices on top, pressing them into the dough slightly.
Bake in the center of the oven until firm and lightly golden, 25 to 30 minutes, rotating the pan halfway through. Let the scones cool for 15 minutes, then remove and discard the parchment paper.
Preheat the broiler and position the rack 8 inches from the heat. Working over a compost bowl, generously sprinkle each scone with the sugar. Broil until the sugar is bubbling, about 1 minute, rotating the pan during broiling to ensure even browning. Alternatively, use a kitchen torch to brulee the scones. Let cool slightly before serving.
Propane gas torches are highly flammable and should be kept away from heat, open flame and prolonged exposure to sunlight. They should be used only in well-ventilated areas. Follow torch manufacturer's instructions for use.