For Pastry:
Place flour, confectioner's sugar and salt in the bowl of a food processor fitted with the "S" blade (that's the standard blade). Pulse a few times to combine.
Add butter chunks and pulse until mixture resembles small peas.
Beat egg yolk and cold water together. With food processor running, add the egg/water mixture through the feed tube, only adding enough to make dough "ball"--depending on weather conditions, you may have to add a few more drops of water.
Remove the dough from the food processor, wrap in waxed paper or plastic wrap and keep in refrigerator until ready for use. You can keep this up to 3 days.
Press pastry into a 10-inch quiche/tart pan, bringing pastry up the sides. You may also use a springform pan of a similar size, but only bring the pastry about 1/2 to 1-inch up the sides.
For the Crumbs:
Mix the melted butter, cinnamon and brown sugar well. Add flour, about 1/4 cup at a time until good, firm crumbs are made. You may not have to use all the flour, or you may have to use a tablespoon or so more. Your eye must be the judge of the proper consistency.
For Filling:
Beat cream cheese and sugar until smooth.
Add eggs and beat until very smooth. Stir in sour cream.
Add apple pie filling to cream cheese mixture and just cut a knife through the mixture a few times--you don't want to mix it well, just "marble" it.
Putting It All Together:
Spread on top of crust in quiche pan. Top with crumbs. Sprinkle with sliced almonds.
Preheat oven to 425 degrees. Place pan on a baking sheet, preferably lined with parchment.
Bake at 425 degrees for 10 minutes. Reduce temperature to 350 degrees and bake an additional 30-35 minutes or until center of tart is almost set.
Remove from oven and cool on rack. You may serve this slightly warm or well chilled. However you serve it, drizzle each serving with caramel sauce.