Any player knows that liquorice swirls are among the most frustrating blockers in the game. You do not want them to get amongst the icing, or you will never be able to open up the board. During the first few turns, make moves that are adjacent to several liquorice swirls. This will remove them from the game before they have a chance to interfere your plans. After you have cleared the liquorice that is closest to the two beginning ingredients, do not worry about the rest for now.
Though you would not be able to drop an ingredient out of the board in one turn, thanks to the multi-layered icings, you can still use striped candies as part of a larger combination move. Wrapped candies are for combinations, and also wreak lots of havoc on their own. Combine one with a striped candy to break through lots of icing (or even liquorice) at once.
By far, the most potent icing-removal tool is the moon struck. When triggered, all the candies matching the colour on the left side of the moon scale will be removed, knocking off one layer from all adjacent icing squares. If you have any moon struck boosters, use one immediately after the first moon struck, before the first removed colour comes back. This will do a lot more damage to the remaining icing and make it much easier to create more special candies and/or cascades.