In a bowl, mix pumpkin, egg yolk, maple syrup, 2 tbsp brown sugar, maple extract, half of the pecans and half of the almonds.
Lightly flour the surface of a cutting board and roll pie crust smooth.
Pour pumpkin mixture in the middle of the crust and spread to form a rectangle. Leave about 3” on both sides of the pie, and 1” on the top and bottom clear.
Make diagonal cuts every 1/2 inch down both sides of the pie crust. Lightly brush sides with water.
Fold the top over the pumpkin. Alternate folding left and right pie crust pieces over the pumpkin mixture to form a braid, tucking the bottom flap up under the last side pieces.
In a small bowl, whisk egg white, pumpkin spice, and 1 Tbsp brown sugar. Brush mixture atop pumpkin braid. If desired, drizzle with a little caramel and sprinkle a few more nuts on top before baking (otherwise, just leave them for topping.)
Place danish onto a parchment paper lined oven safe dish and bake for 45 minutes, or until the crust is golden brown.
Remove from the oven. Drizzle caramel and cream cheese icing atop. Sprinkle remaining pecans and almonds. Serve warm with coffee or a pumpkin spice latte!