Preheat oven to 400°F and line a cookie sheet with foil. Wash the beets and place them on the baking sheet. Wrap the foil around the beets and bake for 45-60 minutes, or until cooked through.
When beets are done cooking, remove from the oven and allow to cool.
Reduce the oven temperature to 350°F and grease a bundt cake pan with non-stick baking spray.
Add the cooked and cooled beets to a food processor and pulse until they are finely chopped. Reserve one cup of the beet "pulp" and set the rest aside.
Add the reserved cup of beets back to the food processor. Process again, until smooth and no lumps remain. Add the Greek yogurt, vanilla, and vinegar. Blend until the mixture is completely puréed.
Transfer the mixture into a large mixing bowl and add the eggs, sugar, and applesauce. Mix well. Slowly add the dry ingredients and mix until just incorporated. Set aside for now.
In another bowl, combine all the ingredients for the cream cheese filling. Use an electric mixer to combine everything, beating until light and fluffy.
Pour about ⅓ of the cake batter into the greased bundt pan. Pour all of the cream cheese filling on top. Top with remaining cake batter and spread it evenly over the cream cheese layer.
Use a knife to lightly swirl the cream cheese filling with the cake batter.
Bake for 55 to 65 minutes, or until the center is set, the top is browned, and a toothpick inserted comes out clean. If the cake is starting to brown too quickly, place a sheet of aluminum foil lightly over the top and continue baking until center is cooked through.
Remove the cake from the oven and allow it cool in its pan for about 30-45 minutes. After, invert the cake onto a plate and let it cool completely, about 45-60 minutes.
Once completely cooled, melt the chocolate and coconut oil/butter in 20-second increments, stirring after each one. Microwave until chocolate is completely melted and smooth. Drizzle the chocolate sauce over top of the cooled cake.
Prepare the vanilla glaze by whisking together all of the ingredients in a small bowl. Add additional powdered sugar if mixture is too runny, or add more milk if mixture is too thick. Drizzle on top of the chocolate glaze.