First, prepare the dough: Place the flours, cane sugar, salt and butter in the food processor and pulse until the butter is in pea-like pieces and dough looks sandy, about 10-12 pulses. Then, drizzle the water into the food processor while pulsing, just until dough comes together - it’s quick!
Flour your surface, and knead the dough a few times until it comes together in a flattened disk. If dough feels a bit too sticky, just sprinkle a little more flour. Wrap disk in food wrap and chill in the fridge for one hour.
Preheat the oven to 400 ℉ (200℃). Cut a large piece of parchment and lightly flour it. Place chilled dough on floured parchment and roll out in a circular shape until dough is ¼ inch (½ cm) thick. No need to get it perfect, rustic is what we’re after. Transfer the parchment and dough to a rimmed baking sheet.
In a medium bowl, toss rhubarb with sugar, cornstarch, vanilla, cardamom and black pepper. Pour rhubarb into the centre of the dough, spreading it out leaving about 2 inches (5cm) border. Then, fold that dough over the filling, so it forms a shallow "bowl" over the filling, pressing gently where the dough folds over itself to help seal it.
Bake for 45-55 minutes, until filling looks jammy and bubbly and dough is golden brown and crisp. Check after 45 minutes, and every few minutes after that. Let cool for at least 10 minutes before slicing and serving.
Galette will keep on the counter for a day or in the fridge, wrapped, for up to 3 days.