Preheat oven to 400 degrees. Line a baking sheet with parchment paper. In the bowl of an electric mixer fitted with the paddle attachment, combine flour, butter, sugar, baking powder, and salt. Mix at low speed until the mixture resembles wet sand.
In a separate bowl, whisk together 3/4 cup cream, 2 eggs, lemon zest, and vanilla. Add the cream mixture to the flour mixture, and beat on low speed until just incorporated. Turn out onto a lightly floured work surface, and form into a flat disc, about 8 inches across and 1 1/2 inches thick. Cut into 8 wedges and transfer to prepared baking sheet.
In a small bowl, whisk together remaining egg and 3 tablespoons cream to make an egg wash. Brush scones with egg wash, and sprinkle with sugar. Bake until the tops are golden brown and firm, 40 to 50 minutes.