Preheat the oven to 425 degrees Fahrenheit, and prepare a baking sheet by lining it with parchment paper.
Measure the flour, baking powder, ginger, baking soda, salt, and about 2 tablespoons of sugar into a bowl. Whisk to blend evenly.
In a small, separate bowl, add the grapefruit zest and the rest of the granulated sugar. Using the back of a spoon, or a fork, press them together until blended.
Using a sharp knife, slice the bottom and top off the grapefruit, then cut in half. Over another bowl, cut the flesh away from the membranes, pith and peel, into the bowl.
Cut the butter into small chunks. Add them to the bowl with the flour mixture, cutting the butter in with knives, or a pastry blender. (You can also use your hands). You’ll know you’re done when the mixture resembles a course meal with chunks pea-sized or less.
Stir in the honey and heavy cream – saving 1 or 2 tablespoons of the cream – folding the mixture over until the whole batter is moistened.
Turn the dough onto a floured surface, and knead lightly until all of it is incorporated.
Divide the dough into two parts, one twice as big as the other.
With the larger part, form a 6-inch circle of dough.
Add the grapefruit flesh on top of the circle, leaving a margin of about 1/2 inch around the edges.
Roll the other part of the dough into a 6-inch circle, and set it on top of the first. Press down – it doesn’t matter if the fruit seeps out from in between.
Sprinkle the grapefruit zest and sugar combination on top, gently pressing it into the dough.
Cut the circle, which should end up about 8-inches around, into 6 triangular scones, and set them on the baking sheet.
Bake for about 15 minutes. They should be firm on top, but still soft in the middle.
Let them cool for at least 10 minutes before eating.