Preheat the oven to 400 degrees. Line a large baking sheet with parchment paper.
Whisk together the half-and-half, egg and vanilla bean paste.
In a large bowl, whisk together the flour, sugar, baking powder and salt. Add the cubes of butter and use a pastry cutter or two forks to cut the butter into the mixture until it resembles coarse crumbs.
Add the half-and-half mixture to the flour mixture and mix in until a soft dough forms.
Roll out on a lightly floured surface into a 9×13 rectangle, about 1/2 inch thick.
Cut into 4-5 inch long rectangles, the cut each rectangle on the diagonal, creating a triangle.
Place on the prepared baking sheet and bake for 8-10 minutes or until just golden brown.
Let cool while you prepare the glaze.
For the Glaze:
Whisk together the powdered sugar, half-and-half and vanilla bean paste into a thick glaze.
Place the scones on a wire rack on top of the baking sheet. Drizzle the glaze on top and allow to set.