Step 1Sift the rye and all-purpose flours, sugar and salt into a large bowl, adding back any bits of grain or other ingredients that may remain in the sifter.
Step 2Cut the butter into half-inch pieces and add to the dry ingredients. Rub the flour-coated butter between your fingers, breaking it into smaller bits. Continue rubbing until the butter is in sizes ranging from peas to hazelnuts. The more quickly you do this, the more the butter will stay solid, which is important for the success of the recipe.
Step 3Add the vinegar and sprinkle a few tablespoons ice water over the flour mixture. Working from the outer edge of the flour, mix the ingredients with your hands just to moisten the flour. The dough needs to come together as mostly one lump, with a few shaggy pieces. Squeeze the dough together to see if a ball forms. If it is too dry to come together, add additional ice water, 1 tablespoon at a time.
Step 4Form the dough into a square, then wrap tightly in plastic wrap. Chill the dough in the refrigerator a minimum of 1 hour, preferably overnight.
Step 5Unwrap the dough onto a floured surface. Using a rolling pin, roll out the dough to form a rectangle about 8 1/2 by 11 inches. The dough will be crumbly and rough around the edges. Don't worry; it will come together during the rolling.
Step 6Fold the dough into thirds, like a letter. Turn the dough so that the seam is at the top. Again roll the dough into an 8 1/2-by-11-inch rectangle and again fold into thirds. Repeat again, then wrap the dough in plastic and chill for 1 hour or up to 3 days before using.
Step 1Cut the apricots in half and discard the pits. Put the apricots into a large bowl, add the sugar and stir to coat. Pour one-half cup of apricot jam over the top and stir again. The apricots should be lightly coated, with just a dab of jam sticking to the center of each.
Step 2In a separate bowl, gently stir one-fourth cup of jam with the boysenberries, being mindful to keep the berries whole.
Step 3To shape the dough, divide it in half. Keep half chilled while the other half is being shaped. Flour the work surface and roll the dough into a rough circle about 15 inches in diameter. Transfer the circle of dough to a baking sheet lined with parchment.
Step 4To form the tart, smear one-fourth cup of jam at the bottom of the tart. Pile half of the apricots and half of the boysenberries into the center of the dough, tucking the boysenberries into the nooks and crannies of the apricots. Fold an edge of the dough toward the center to cover the fruit; about 3 inches of crust should be showing. Continue folding the edge of the dough toward the filling and over to create folds. Each one will look different.
Step 5Once the tart is formed, it should be about 9 inches in diameter. Using the same procedure, shape the second tart on a separate parchment-lined baking sheet. Freeze both tarts for a minimum of 1 hour.
Step 6While the tarts are freezing, heat the oven to 350 degrees.
Step 7Stir the sugar and cinnamon together. Whisk the egg to make an egg wash. Take the baking sheets out of the freezer and brush the edges of the dough with the egg wash. Sprinkle half of the cinnamon sugar evenly over each of the tarts, on both the crust and the fruit. Don't skimp -- it creates a great crust.
Step 8Bake, rotating the pans halfway through, until the crusts are dark golden brown and blistering, the jam is bubbling and perhaps some juice has run from the tart and caramelized on the parchment paper, about 60 to 70 minutes.
Step 9Serve the tarts warm from the oven or later that day. The unbaked tarts will keep, well wrapped and frozen, up to 1 month.