For Crust: Place almonds and 1 tablespoon powdered sugar in a food processor. Pulse until the nuts are finely ground.
In bowl of electric mixer fitted with paddle attachment, cream butter, ground nuts and salt on medium speed until well-combined. Slowly add remaining powdered sugar and flour and mix well.
Add the egg yolk and mix until incorporated.
Shape dough into a ball and flatten into a disc. Wrap with plastic wrap and refrigerate for two hours or overnight.
Place the dough in between two sheets of plastic wrap or parchment paper and roll it out to about 1/4-inch thick round.
Place in a 9-inch tart pan, trim the edges. Prick the dough with a fork and refrigerate 30 minutes up to 2 hours. (you can even freeze the dough in the tart pan at this point and let thaw in the fridge overnight when you are ready).
In the meantime, prepare the applesauce.
For compote: On a flat surface, cut the vanilla bean in half lengthwise without cutting all the way through and scrape the seeds from the pods with a pairing knife. Place them in a large saucepan along with the sugar. Set aside.
Core and roughly chop the apples. Add them to the vanilla and sugar mixture along with the water.
Bring the mixture to a simmer over medium heat. Turn the heat down, cover and let the apples stew for about 1 hour.
Check every 20 minutes to and add water to the mixture if the liquid evaporates faster than the apples can cook.
Remove from the heat and let cool to room temperature. Scoop about 1 1/2 cups applesauce inside the prepared tart pan.
For Topping: Preheat oven to 350F and position a rack in the middle.
In a small bowl, rub together the sugar and lemon zest so that the citrus natural oils can flavor the sugar.
Core and thinly slice the apples. Decoratively arrange the slices over the compote and sprinkle evenly with the sugar. Scatter the butter over the tart shell.
Bake for 35-40 minutes or until the top apples are golden brown.
2 (16-oz) packages frozen blackberries, thawed and drained
To make the crust and topping, preheat the oven to 350 degrees. Grease a 9x13 inch baking pan.
Combine the flour, sugar, and salt in the bowl of a food processor. Pulse a few times to mix. Cut the butter into 1/2-inch cubes, and add to the flour mixture. Process until the butter is evenly distributed but the mixture is still crumbly, 30-60 seconds.
Reserve 1 1/2 cups of the mixture to use as the topping. Press the remaining mixture into the bottom of the pan, and bake 12-15 minutes. Cool for at least 10 minutes.
To make the filling, whisk the eggs in a large bowl, then add the sugar, sour cream, flour, salt, lemon zest, and almond extract. Gently fold in the berries and spoon the mixture over the crust. Sprinkle the remaining flour mixture evenly over the filling, and bake 45 to 55 minutes.
Cool at least 1 hour before cutting into bars, or scoop out of the pan to serve cobbler-style.