Preheat the oven to 350°F and line a 13”x18” half baking sheet with parchment paper (allowing a few inches to hang over the edge), spray with cooking spray, and set aside.
For the chocolate sponge cake layer, sift together flour, baking soda, salt, sugar, and cocoa powder in a large mixing bowl. Add in the eggs and milk. With an electric mixer, beat on medium until well combined.
Pour cake mixture onto your baking sheet with parchment paper. Spread into an even layer. Bake for 15 to 20 minutes or until a toothpick inserted comes out clean. Allow the cake to cool for 3 to 4 minutes.
While the cake is baking in the oven, make the buttercream filling layer. In a large mixing bowl, add unsalted butter and cream butter on low speed until pale and creamy.
Slowly add in 1 cup of powdered sugar, 1 tbsp heavy cream, and cocoa powder while mixing on low for about 3 minutes. Add in remaining amounts of sugar and cream, alternating a little at a time
Add in vanilla and salt and beat on medium-high for about 2 to 3 minutes until frosting is light and fluffy. If your frosting needs to be thinned out, add cream in small amounts at a time. If your frosting needs to be thicker, add more powdered sugar in small amounts at a time. Set aside.
Make simple syrup while the cake is in the oven and/or cooling. Pour water and granulated sugar into a small saucepan and stir. Bring to a boil over high heat, stirring until sugar dissolves. Remove from heat and allow to cool.
Once your cake has cooled for a few minutes, fold the edge of the parchment paper over the short edge and roll it up. Allow it to cool for an additional 10 to 15 minutes.
Unroll the cake and cut away any hard edges. With an offset spatula, spread the buttercream filling in an even layer all over the cake, reserving a few tablespoons (to later attach the offshoot branch). Roll the cake, loosely cover with foil, and chill in the refrigerator for about 15 minutes.
While the cake is chilling, make garnishes. Dip sprigs of rosemary and fresh cranberries in simple syrup and then in granulated sugar until well coated. Set aside.
Remove chilled cake from the refrigerator and slice on a diagonal, about 3 to 4 inches from the end for your log. Slice any rough ends off of the log to make them straight. Transfer the cake to a serving platter and attach the log on the side with the reserved buttercream.
Next, make the chocolate ganache. Place semi-sweet chocolate chips in a heat-safe glass bowl. Pour ½ cup heavy cream into a microwave-safe bowl or coffee mug and heat for 50 seconds (watch this closely so it doesn’t overflow). Pour over chocolate chips and set aside for 4 to 5 minutes to allow the chips to melt. Whisk slowly into a ganache.
With an offset spatula, spread ganache onto the yule log cake. Use the spatula to create texture in the ganache to make it look like bark on a tree.
Add sugared cranberries and rosemary on top of and around the cake. Lightly dust with powdered sugar.
Loosely cover with foil and chill for an additional 15 to 20 minutes. Slice and enjoy!