Begin by preheating the oven to 350 degrees F. Grease two 15x10x1-inch pans with baking spray, cover with parchment paper, and then spray again.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In the bowl of an electric mixer, beat the eggs on high for 3-5 minutes, until pale in color. Continue beating as you slowly add the sugar. Once combined, add the oil, buttermilk, vinegar, vanilla extract, and almond extract. Beat to incorporate. Finally, beat in the dry ingredients until just combined.
Divide the batter evenly between the two prepared baking pans. Tilt the pan (or spread with a spatula) to even out the batter.
Bake for 12-15 minutes or until the cake springs back when touched.
While the cakes bake, lay two tea towels out on your countertop and sprinkle each towel with powdered sugar.
When the cakes are done, immediately invert them onto the prepared towels. Remove the parchment paper and then roll the cake in the towel starting at either of the narrower ends. Set the rolled-up cake on a wire rack to cool completely. (This step is important because it will prevent your cake from cracking later when you reroll it after it's cooled.)
In the meantime, prepare your filling. In the bowl of a stand mixer, beat the cream cheese, butter, and salt until smooth. Add the vanilla and almond extracts and beat to combine. Gradually beat in the confectioners' sugar and white baking chocolate until smooth. Divide this frosting evenly into three bowls. (I added a bit of brown gel food color to two of the bowls because I would be using it as the filling frosting for the cakes.)
Once the cakes have cooled, unroll them. Using two of the three bowls of frosting, spread one bowl over each of the cakes to within 1/2 inch of the edge. Roll them up again, without the towel. Place both rolls seam side down onto a large platter and refrigerate until the filling has set. This will take about 2 hours.
Once the cakes have cooled, trim off the edges of each cake. Set one cake roll on a platter. Then cut the second cake roll to create the branches for the other cake roll. Trim the cake branches so they fit snuggly against the first cake roll.
Divide the remaining bowl of frosting into two bowls. Use a touch of brown gel food coloring to dye the frosting in one of the bowls; leave the frosting in the other bowl white. Spoon each frosting into a separate piping bag, cut off one corner of each, and pipe lines on the cake to resemble bark. Fill in any areas where the cake connects.
Garnish the yule log with sprinkles, sugar pearls, and coarse sanding sugar for sparkle.
To create chocolate mushrooms, put melted white chocolate, melted milk chocolate, and melted peanut butter chips into separate piping bags. Pipe the desired shapes onto wax paper. Sprinkle with coarse sanding sugar or add sugar pearls to the mushroom shapes before the chocolate sets for added interest. Allow the chocolate to cool completely, and then tuck them into your yule log.