Line a sheet pan with parchment paper. In a liquid measuring cup (or medium mixing bowl), 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 10 to 12 times, until it comes together, adding a little flour as necessary. Pat the dough into a square and roll it into a 12-inch square, dusting with flour as necessary. Fold the dough in 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-inch 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-inch rectangle.
With a sharp knife, cut it crosswise into four equal rectangles, then cut each rectangle diagonally into two triangles. Transfer the triangles to the prepared sheet pan. Freeze the scones for 30 minutes. (This is important!)
Meanwhile, position an oven rack in the middle of the oven and preheat to 375 degrees.
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.
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.
Use an offset spatula to spread each scone with the glaze (below).