Center the oven rack and preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, baking powder, salt, and sugar. Pour the vanilla extract into the cream, and stir briefly to combine.
While stirring slowly and gently, slowly add the cream mixture to the flour mixture. If dry bits of flour remain in the bottom of the bowl, moisten them with an extra tablespoon of cream.
On a lightly-floured work surface, gather the dough into a ball, and then flatten the ball into a disk. Lightly dust the top with flour. Using a rolling pin, form the dough into a circle that is approximately 1 inch thick.
Using a floured 2-inch-diameter biscuit cutter, cut out rounds, re-rolling scraps as necessary. Put the rounds on the prepared baking sheet, spacing them 1 to 2 inches apart. Brush tops with cream, and then sprinkle with Demerara sugar.
Put the baking sheet in the freezer for 15 minutes. Chilling the dough this way will insure that the scones maintain their upright posture during baking.
Bake the thoroughly-chilled scones in the preheated oven until they puff, and their tops color appetizingly -- 12-15 minutes. Cool on a wire rack. Serve with clotted cream (or whipped cream) and jam.