In a food processor, pulse the flours, granulated sugar, and salt until incorporated, about 5 pulses. Add the butter and pulse until incorporated but still with lots of pea-size pieces, 10 to 15 pulses (make sure not to overprocess). Add the cream and pulse until the mixture is moistened but still clumpy and not fully unified, 10 to 15 more pulses. (If the dough feels too dry and does not stick together between your fingers, add more cream by the teaspoon until you achieve a sticky texture.) Transfer the dough to a floured work surface and gently gather it into a ball. Form a 6 x 1-inch disc out of the dough, wrap tightly in plastic wrap, and refrigerate until firm, at least 2 hours and up to 24.