Prepare the ingredients: grate the zucchini and cheese. Gently squeeze the zucchini to remove any excess water.
In a large bowl, whisk together the flour, baking powder, salt, and sugar.
Dice the butter and add it to the flour mixture. Using your fingertips or a pastry blender, cut the butter into the flour until the mixture resembles coarse crumbs. This will help the scones be light and crumbly.
Add the grated zucchini and cheese to the dough, and mix until evenly distributed.
In a small bowl, whisk the egg with half of the heavy cream. Pour the egg-cream mixture into the dry ingredients, and quickly mix until just combined.
Shape the dough into a 1.5-inch (3-4 cm) thick circle. On a lightly floured surface, cut the circle into 6-8 wedges.
Place the wedges on a baking sheet lined with parchment paper, and brush them with the remaining heavy cream for a glossy finish.
Bake in a preheated oven at 350°F (180°C) for 15-20 minutes, or until golden brown on top.
Let the scones cool slightly before serving with fresh butter or a dollop of yogurt.
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