Beat the egg yolks, coconut oil, and sugar in the bowl or your stand mixer using the paddle attachment. Beat until it's well combined and has a crumbly look to it.
Add the cocoa powder, cinnamon, sour cream, and vanilla extract to the egg yolk mixture and mix on medium speed until combined.
In a small prep bowl, combine the baking soda and vinegar and mix just until it becomes foamy. Then add it to the sugar and sour cream mixture.
Add the rye flour and all-purpose flour to the mixer bowl and mix on medium speed until all the ingredients are well combined.
Scoop out the dough using a medium-sized cookie scoop. The dough will be very sticky, therefore coat your hands with coconut oil and shape each scoop into round balls.
Place each cookie onto a greased baking sheet and bake at 365 degrees Fahrenheit for 18 minutes.
Meanwhile, work on the glaze. In a bowl, beat the egg white with a fork just until slightly bubbly. Then add the powdered sugar and peppermint extract. Beat until the consistency of the glaze becomes runnier. Depending on the size of the egg, you may need less or more powdered sugar. Add 1/4 cup at a time.
Once the cookies are baked, let them cool for about 6 minutes before coating them with the glaze. You don't want them to cool for too long though. Coating the cookies with the glaze while they are slightly warm, will give them a shinier look.