Preheat oven to 400F and line a large sheet pan with parchment paper. Set aside.
In a large bowl, combine flour, baking powder, and salt. Use your fingers or a pastry cutter to work cold butter into flour mixture until butter is in pea-sized clumps.
In a small separate bowl, whisk yogurt, 1/4 cup heavy cream, milk, and honey until smooth. Create a well in the center of flour mixture and pour yogurt mixture into well. Very gently fold and knead until you get a shaggy dough (add a few extra splashes of milk if dough is too dry)
Turn dough onto a floured surface and pat into a 1-inch thick square. Cut square into 4 pieces using a benchscraper or knife and stack the pieces on top of one another. Use your hands to flatten dough back down to 1 inch and roll into a 7x5-inch rectangle.
Cut rectangle into 6 equal squares and place squares on prepared baking sheet. Brush squares with remaining 2 tablespoons heavy cream and sprinkle tops with sugar.
Place pan in the freezer for 15 minutes to chill the fats in dough before baking.
Remove pan from freezer and bake shortcakes at 400F 15-20 minutes until golden brown. Allow shortcakes to cool on pan 10 minutes, then transfer to a wire cooling rack.