Once the cake has cooled, cut the cake into three 6" diameter circles -I used a small serving bowl as my guide. Save the rest of the cake mixture for cake pops (or enjoy it now, who am I to judge?). See how the pros do it here: https://sallysbakingaddiction.com/homemade-cake-pops/
Place the bottom layer of cake on a serving tray. Top with approximately 1/4 cup of frosting, and repeat for each of layer. Crumb coat the cake and chill for minutes.
Frost the sides of the cake. It doesn't need to be smooth, the texture helps create a more realistic birch tree! Also, the rougher texture helps hide blemishes, and accidental touch marks ...which is perfect for cake noobs like myself.
Place a small amount of gel food colouring into 3 individual, small dishes -one with black gel colouring, and two with brown. It's easy to over do it with color here, especially with black, so add a small amount at first. You can always add more later. Add a touch of hot water (½ tsp or less) into each dish, enough to thin the gel to make it easier to apply.
Take ½ cup of frosting and place into a piping bag (or a ziplock with the corner cut off works just fine too). Mix in one of the brown gel food colorings. On the top of the cake, pipe in circles, starting at the center and working your way outwards to mimic the rings of a tree.
Take a toothpick, or a unused paintbrust and paint on the patterns and lines of the birch tree with the remaining brown and black food coloring. Take a spatula to blend and smudge the lines for a more natural look.
Add your finishing touches! Twigs, pinecones, figurines, or a hand 'carved' heart.