Line a sheet pan with parchment paper. In a medium bowl or liquid measuring cup, whisk together the mashed bananas, heavy cream, egg, and vanilla. Refrigerate until ready to use.
In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt.
Add the butter to the dry ingredients, and use a pastry cutter to cut in the butter until the flour-coated pieces are the size of peas. Add the refrigerated wet ingredients and fold with a spatula until just combined.
Transfer the dough to a generously floured surface and knead ten to twelve times, until it comes together, adding a little flour as necessary (the dough will be sticky). Pat the dough into a square and roll it into a 12 in [30.5 cm] square, dusting with flour as necessary. Fold the dough into thirds, like a business letter. Fold the dough in thirds again by folding in the short ends, making a square. Transfer it to the prepared sheet pan and put it in the freezer for 10 minutes.
Return the dough to the floured surface, shape it into a 12 in [30.5 cm] square, and fold the dough in thirds again. Turn over the dough, so it's seam-side down, and gently roll out the dough into a 12 by 4 in [30.5 by 10 cm] rectangle.
With a sharp knife or bench scraper, cut the dough crosswise in to four equal rectangles, then cut each rectangle diagonally into two triangles, for a total of eight scones. Transfer the triangles to prepared sheet pan. Freeze the scones for 30 minutes, or up to two weeks.
When ready to bake, position an oven rack to the middle of the oven and preheat the oven to 375F [190C].
Brush the tops of the scones with a little heavy cream, making sure it doesn't drip down the sides. Place another sheet pan under the scones, so the pans are double-stacked (this helps prevent the bottoms of scones from browning too quickly). Bake the scones, rotating the stacked pans halfway through, until the tops and bottoms are light golden brown, 18 to 25 minutes. Transfer the top sheet pan to a wire rack and let the scones cool slightly.