MAKE THE FILLING: In a medium bowl add the almond paste, softened cream cheese, and sugar. Beat with a handheld mixer on medium speed until smooth. Cover the bowl with plastic wrap and refrigerate until ready to use.
MAKE THE DOUGH: In a large measuring cup whisk together the milk, melted butter, honey, egg yolks, and vanilla, and set aside.
In the bowl of a stand mixer fitted with a hook attachment, add 4 3/4 cups of flour, yeast, and salt. With the mixer on low speed, add the milk mixture and mix until the dough comes together, about 2 minutes, scraping down the sides of the bowl halfway through mixing.
Increase the mixer speed to medium and knead until the dough is smooth and shiny about 5 to 7 minutes. Add up to ¼ cup of flour, 1 tablespoon at a time, if the dough is not clearing the sides of the bowl after 5 minutes.
Turn the dough out onto a lightly floured surface and knead by hand to form a smooth round ball, about 1 minute.
Place the dough in a lightly oiled large bowl and wrap tightly with plastic wrap. Let the dough rise in a warm place until doubled in size, 1 to 1 1/2 hours. If your kitchen isn’t very warm, then preheat the oven to 170º and then turn it off. Put your dough in the oven to rise.
FORM THE DOUGH: Line 2 baking sheets with parchment paper, and set aside. On a large lightly floured piece of parchment paper, divide the dough into 2 equal pieces. Working with one piece of dough at a time, roll it out into an 18 x 9-inch rectangle. Spread half of the filling in a 1-inch wide strip just above the bottom edge of the dough.
Roll the dough into a tight log, and pinch the seam closed. Transfer the log, seam side down, to one of the prepared baking sheets. Repeat with remaining dough and filling.
Shape each dough cylinder into a ring. Make about 11 cuts around the outside of the dough using a paring knife. Each cut should be about 1 to 1 ½ inches apart. Twist each piece of dough cut side up.
Lightly spray the coffee cakes with cooking spray, wrap loosely in plastic wrap, and let them rise in a warm place until they have nearly doubled in size and spring back slowly when indented with a finger, about 1 to 1 ½ hours.
TOP AND BAKE: Adjust the oven racks to the upper-middle and lower-middle positions and heat the oven to 375ºF.
Brush the rings with egg whites and sprinkle with almonds. Bake until deep brown, about 25 minutes, switching and rotating pans half-way through baking. Remove the coffee cakes from the oven and place on a wire rack and cool for 1 hour.
MAKE THE ICING & FINISH: Whisk the sugar, softened cream cheese, milk, and vanilla together in a small bowl until smooth, and then drizzle it over the cakes before serving.