Heat oven to 450ºF. Line a half-sheet pan with parchment paper and set aside.
In a large mixing bowl, combine the flour, baking powder, baking soda, sugar, and salt. Using your fingertips, rub the chilled butter and shortening into the dry goods until the mixture resembles coarse crumbs. Mix in the half-and-half and stir until a sticky batter forms.
Using a large spoon, drop 8 large dollops of batter onto the prepared half-sheet pan. Brush with melted butter and sprinkle with additional sugar. Bake until golden brown, about 15 minutes.
Turn out into a kitchen towel-lined basket and cool 10 minutes before splitting and topping with macerated strawberries and whipped cream.