Combine all dough ingredients except the ice water in a large bowl. With clean hands, blend the mixture together until it looks like coarse meal with some lumps in it.

Sprinkle ice water over mixture and stir lightly with a fork. Squeeze a handful of dough together. If it doesn't keep together, add a bit more water.

Form the dough into a chubby disk about 5 inches across. Wrap the disk in plastic wrap and chill for about an hour. Once chilled, take out the disk and put it on a well floured board. Sprinkle some flour onto the top of the disk. Thump the disk with your rolling pin several times. Turn it over and thump the other side. Sprinkle more flour onto the top of the crust if needed to keep the pin from sticking and roll the crust out from the center in all directions so it's about 11 inches in diameter.

Carefully transfer the rolled out dough onto a parchment lined baking sheet. Heat oven to 400 degrees.

Combine the almond paste and sugar in a food processor and blend until smooth. Add the butter, salt, rum and egg yolk and process until everything is incorporated. Remove the mixture from the food processor and use a spatula to spread the mixture on the dough in a circle, leaving about 2 inches un-covered.

Combine all the ingredients for the fruit section in a bowl and toss together. Transfer the fruit on top of the frangipane layer.

Gently fold the crust over the fruit, pleating to hold it in. Brush the crust generously with egg wash mixture and sprinkle some extra sugar on the crust.

Bake for 35 to 45 minutes, until the filling bubbles up vigorously and the crust is golden. Cool for at least 30 minutes on wire rack. Serve warm or at room temperature with a dollop of creme fraiche or vanilla ice cream.