Combine the flours, sugar, salt and yeast in a mixing bowl and stir together. Next, add this mixture to a food processor. Add the butter and pulse-process a dozen times or so. You’ll want the chunks of butter to be chopped to half-sized pieces.
Combine the egg and milk into a large mixing bowl and briefly stir together with a table fork or whisk if you have one. Add the dry ingredients to the egg mixture and stir together without over-mixing. Briefly knead the dough by hand then place on a hard, clean work surface. Gently pat the dough into a square or rectangle shape and wrap and seal with kitchen wrap. Chill in the fridge for 6 to 48 hours.
On a hard, clean, and lightly-dusted work surface, use a rolling pin and form the dough into a rectangle, about 9 x 15 inches in size. Take the short ends of the dough and fold in toward the center (using about one third of the dough on each end.) Turn the rolled and folded dough by 90 degrees and repeat this process using the same dimensions. Use kitchen wrap to wrap and chill for 30 minutes.
Repeat the above step 1 more time. Now you have the option of using the dough, storing it in the fridge for 48 hours (wrapped and sealed,) or freezing it for up to 3 months.
For the Kringle Filling
Grab your butter, brown sugar and nuts and combine them all together in a large bowl.
Shape and Bake
Use some parchment paper to line two large cookie sheets. Take your chilled dough and evenly divide it in half.
Use a hard, clean work surface lightly dusted with flour and shape each piece of dough into a rectangle, approximately 5 x 20 inches in shape. Evenly spread about a half cup of the filling down the center of each piece of dough, leaving about a 2 1/2 inch border on each side.
For each piece of dough, fold one long side over the filling and use the egg whites to brush an egg wash over the other unfolded side and both ends. Now take the unfolded long side and fold it over to the other side as shown in the photos above. Use your fingers to pinch and tightly seal the seams on the side and on the ends.
At this point the kringle dough may have retracted and gotten shorter. If necessary, gently stretch it out until it is between 20 and 24 inches in length. Take the two ends of each piece of folded dough and bring them together in the shape of a circle or an oval (like a race track.) Seal the ends together by using your fingertips to press and tightly seal. Now, take each circular-shaped unbaked kringle and place on the parchment paper-lined baking sheet. Invert them (flip) so the seam is facing downward. Cover with a kitchen towel or kitchen wrap and place the cookie sheets in a warm place. Allow the dough to rise for about 2 hours
You’ll bake the kringle at 375 degrees. As always, be sure your oven is preheated. Before you bake them, apply an egg wash to the outside. You’ll want to bake these to a golden-brown color about 20 minutes. Turn the baking sheets and switch racks (from top to bottom) at about 12 minutes. This will ensure that your kringle bakes nice and evenly.
These will be very hot when you take them out of the oven. To get rid of any air pockets between the filling and the crust, gently place one baking sheet on top of the other kringle (and then repeat with the other one.) Now place each one to a wire cooling rack.
Make the Frosting and Icing
In a small bowl, stir the powdered sugar, vanilla, sea salt and 3 to 4 tablespoons of water or milk. Use an off-set spatula or rubber one and evenly spread the icing over the tops of the pastry and allow it to completely dry.
For the salted caramel glaze: In heavy small saucepan melt butter over medium-low heat. Stir in packed brown sugar and granulated sugar. Bring to boiling, stirring constantly. Then stir in whipping cream and return to boiling. Boil 2 minutes, stirring constantly. Remove from heat; stir in sea salt. Cool completely. Then, drizzle the glaze over the icing.
Notes
This makes two kringles.
Substitute walnuts for pecans if desired.
You can substitute lemon juice for vanilla extract in the frosting.
Oven temperatures vary. Check the kringle at 15 minutes and if it is brown and looks done, take it out of the oven.