For the dough: Place the butter, sugar, and salt in a large mixing bowl. Bring the milk to a simmer on the stove or in the microwave and pour over the ingredients in the bowl. Stir briefly and allow to cool to lukewarm., When the mixture has cooled, stir in the yeast, egg, and vanilla. Add the flour and mix until a soft dough forms. Knead the dough for 6 minutes in a mixer or 8 minutes by hand. Cover and let rise until doubled, about 45 minutes to 1 hour., For the filling: In a medium bowl, whisk together the egg white, sugar, and salt. Stir in the toasted almond flour and all-purpose flour., Add the melted butter, almond extract, and 2 teaspoons of milk. The filling should be quite thick but spreadable, about the consistency of peanut butter. Add a little more milk if needed to achieve the desired consistency., To assemble: Roll out the dough on a greased surface to a rectangle 24"wide and 10" tall. Spread the filling over the dough in a thin layer, leaving 1" of both long edges uncovered. Roll up the dough from one long edge to the other, pinching it together to seal it., Transfer the dough to a piece of parchment, seam side down, and form into a circle, tucking one end inside the other. Pinch this seam together also. You should have a circle in the center roughly 4" in diameter., Slice the dough from the outside edge three-quarters of the way through, leaving the center intact. Repeat in 1 1/2" increments all the way around the dough (spin the piece of parchment with the dough on it to make this easier)., Turn the slices on their sides, pulling every other one to the inside of the circle. Cover with greased plastic and let rise once more until puffy, about 45 minutes., Preheat the oven to 350°F., When the dough has risen, brush it all over with the egg wash and bake for 24 to 26 minutes, until golden brown and the center reads 190°F when measured with a digital thermometer. Remove from the oven and let cool on a rack., For the glaze: Combine all the ingredients except for the almond slices. Drizzle over the slightly warm coffee cake. Sprinkle with toasted almonds., Store, well-wrapped, for 3 days at room temperature, or freeze for up to 3 months.