Preheat oven to 400F. Line 2 cookies sheets with parchment.
Beat the half-and-half (or whipping cream) and egg in a small bowl until blended.
Mix flour and baking powder together in a medium-sized bowl. Add the butter and cut in with a pastry blender or fork until mixture resembles cornmeal.
Add the apricots and sugar to the flour mixture. Stir with a fork until mixed.
Add the egg mixture and stir until a soft dough forms.
Turn the dough out onto a lightly floured surface and pat into a 9” circle. The dough will be sticky, so put some flour onto your hands too.
Cut the circle into 12 triangular wedges. Place wedges about a 1/2” apart on the cookie sheets. If you opt to drop small circular mounds down instead, also place 1/2” apart on cookie sheets.
Sprinkle a little sugar on top for a slight crunch.
Bake for about 12-15 minutes at 400F until browned.
Remove to a wire rack to cool.