Create molds to use in making the fondant appliques with the " Knead-a-Mold" silicon-mold system and wooden or plaster architectural reliefs or moldings (Decorators Supply has a large selection).
Assemble tiers: Trim tops of 15-inch cake layers to be level, and cut each layer in half horizontally (for 4 layers total). Set 1 layer on same-size foam board. Spread a layer of mint buttercream over top. Repeat with remaining 15-inch layers, spreading buttercream between the layers. Spread a thin layer of buttercream over top and sides to seal in crumbs, and refrigerate until firm, 30 minutes to 1 hour. Repeat to make remaining tiers (cut 7- and 12-inch cakes in half horizontally to make extra layers), spreading remaining layers with buttercream, and placing the bottom layer of each tier on corresponding-size foam board.
Cover tiers (see note under ingredients for fondant amounts): Knead food coloring into the fondant for each tier, adding tiny amounts at a time until the desired color is reached. For each tier, roll out fondant to 1/8 inch thick. Drape fondant over a rolling pin; center and place it on the tier. Starting at the top, smooth fondant onto cake with your hands. Cut away excess with a pastry wheel. Tiers can be stored at cool room temperature up to 24 hours.
Stack the tiers: Insert 1 dowel in high spot on 15-inch tier. Grasp with dowel cutter just at top of cake, and pull out. Cut dowel, and use it to trim 11 more dowels to the same height. Insert dowels into the tier, arranging 8 evenly spaced about 2 inches from edge, and 4 in a square near the center. Repeat for all tiers, inserting 8 dowels in the 12-inch tier, and 6 dowels in the 10-inch tier; place 3 dowels in the top tier to support the small compote used as a topper. Stack tiers on cake board, largest to smallest.
Make appliques: Dust molds lightly with cornstarch; press fondant firmly into mold and smooth the back. Trim excess fondant away at edges of mold shapes, and unmold. Attach appliques to coated tiers with royal icing. Use royal icing to pipe other details directly onto cake.