Let the crust stand at room temperature for 20 minutes to soften slightly. Postion rack in the top third of the oven and preheat to 375℉.
Place the crust dough between sheets of parchment paper. Roll out to a 10" diameter round, turning over occasionally and freeing the parchment as needed, dusting with flour if sticking. Remove the top sheet of parchment and sprinkle ½ cup of the chopped nuts evenly over. Replace the top sheet of parchment and roll the crust out to an 11" round, embedding the nuts into the crust.
Keeping the crust between the sheets of parchment, transfer it to a heavy large baking sheet, arranging nut side down. Remove the top sheet of parchment, letting the crust remain on the bottom sheet. Arrange the peaches in the center of the crust, leaving a 1½ to 2" boarder. If your peaches weren't sweet, drizzle a little honey over the peaches. Using the parchment as an aid, gently fold the crust edges over the edges of the peaches, gently pleating as needed.
Mix the brown sugar and cardamom (if using). Arrange the blackberries (if using) over the peaches. Brush the crust edges with egg to glaze. Sprinkle the remaining chopped nuts (using as many or few as you like) over the fruit and crust, then sprinkle the brown sugar over the fruit and crust.
Bake the tart until golden brown, about 35 to 40 minutes. Cool the tart on the pan for 20 minutes. Carefully slide a spatula between the tart and parchment to free the crust. Using the bottom of an 11" tart pan, slide it under the tart and gently transfer to a platter.
To serve, cut the warm or room temperature tart into wedges and transfer to plates. Top each with a dollop of Greek yogurt and then drizzle with honey.