Combine the yeast and sugar in the bowl of a stand mixer fitted with a dough hook.
Add the melted butter and warm water. Beat at low speed for 1 minutes. With the mixer running, add the egg yolks, then beat for 1 minute at medium-low speed. Add the flour, salt, 1 teaspoon of the cinnamon, nutmeg, and lemon zest and beat until everything is incorporated. Increase the speed to high and beat until the dough pulls away from the sides of the bowl, forms a ball, and starts to climb up the dough hook. Remove the dough from the bowl. Using your hands from the dough into a smooth ball. Lightly oil a bowl with the vegetable oil. Place the dough in the bowl and turn it to oil all sides. Cover with plastic wrap and set aside in a warm, draft-free place until doubled in size, about 2 hours.
FOR THE FILLING:
In a large mixing bowl, combine the cream cheese and 1 cup of the confectioners' sugar. Blend by hand or with an electric mixer on low speed and set aside. Line 2 baking sheets with parchment paper. Turn the dough out onto a lightly floured work surface and divide the dough into fourths. Using your fingers, pat it out into a rectangle. Spread the filling lengthwise over the bottom half of each dough, then flip the top half of the dough over the filling. Seal the edges, pinching the dough together. Shape each dough into a flat cylinder and form into a ring and pinch the ends together so there isn't a seam. Insert the bean into the ring from the bottom so that it is completely hidden by the dough. Cover the rings with plastic wrap and place in a warm, draft-free place. Let the dough rise until double in size, about 20 to 25 minutes.
Preheat the oven to 350 degrees F.
Brush the top of the risen cake with 2 tablespoons of the milk. Bake until golden brown, about 15 minutes. Remove from the oven and let cool completely on a wire rack.
Make the icing: Combine the remaining 3 tablespoons milk, lemon juice, remaining 1/4 teaspoon cinnamon and the remaining 3 cups confectioners' sugar in a medium size bowl. Stir to blend well. With a rubber spatula, spread the icing over the top of each cake.
Slice each cake into individual slices and serve.