Grease a baking sheet or line with parchment paper.
In a large bowl, whisk together the butter, vanilla, nutmeg, cinnamon, brown sugar until light and fluffy, and pecans and stir to combine. Set aside.
Lightly dust a cutting board with flour. Unroll and lay out the puff pastry. Dust with flour on top. With a rolling pin, roll the puff pastry to 25 centimeters wide by 38 centimeters long. Cut in half vertically making two 12x28 centimeter pieces.
Place half of the filling in a long strip along the center of each puff pastry. Fold one of the long edges over the filling. In a small bowl, add the egg and one tablespoon of water and whisk to combine. Brush the other long edge with egg wash, fold over the top to cover. It should be in the shape of a log. Repeat with the second piece of puff pastry. Reserve additional egg wash.
Carefully place both pecan logs onto the greased baking sheet. Brush openings with egg wash and press together to seal and form a ring. Place in the refrigerator to chill for 30 minutes.
Brush the top of the ring with the remaining egg wash. Bake until golden brown, about 20 minutes.
Allow the kringle to cool completely. To make the glaze, combine the confectioner’s sugar, milk, and vanilla. Drizzle over the cooled kringle Garnish with flaky sea salt.