Once the butter is chilled put the flour, salt, baking powder, and sugar in a food processor and pulse a few times to incorporate and aerate the flour a bit. Drop in the butter and shortening, and pulse about 10 times, until the mix resembles wet sand and most of the butter is cut down to the size of peas (though don’t worry if some pieces are larger). Take off the lid of the processor, pour the cream evenly around the flour mixture, return the lid, and pulse a few more times to combine. It should hold together when pinched. Turn it out onto a lightly floured surface, form it into a ball, roll into a disc, and cover tightly with plastic wrap before stashing in the fridge for at least 1 hour, but up to 3 days.