If it's still Winter time where you live, then it's best to let it thaw.
You can take the daily portion out of the freezer the night before and place it on the refrigerator instead. That will give it time to thaw overnight and be ready to offer.
Also for overall health and hygiene reasons, it would be best to place the mash in proper ice trays and not use the egg cartons.
Your Fenway is a cutie! Good song choice there, "Cherry Blossom Girl" by Air, right?
RIP sweet Tito (Summer 2008 - January 17th 2013).
You are missed and never will be forgotten.
It's always best to allow anything frozen to thaw completely before offering it to your budgies.
The shock of frozen food on a tiny budgie's system can be quite daunting and isn't really good for them.
I agree with aluz that it is better to use an ice cube tray rather than re-purposing an egg carton for freezing in the future.