Hi there - new here! I spent some time searching through posts and didn't see anything that quite fit my problem, so I am going to post it here and hope that you can help me.

I started a hive in April with some Italian honey bees. They grew quite quickly and filled out about 70% of the deep brood box with comb, so (as per various advice online) I added an upper deep for pollen, nectar, and honey storage. However, this deep is filled about 60% with brood and absolutely no food, aside from a few rows on one or two of the frames. It's about 46 degrees out and Fall is definitely here. It appears as though they kicked the drones out (bodies around the entrance), so things seem right, but they are facing a cold Fall and Winter without food! They spent the whole summer rearing brood and foraging for day-to-day survival. I am not sure if they ran out or time or if something is wrong, but they will not last in their current situation.

How do I help my girls survive the winter? I went into emergency mode and mixed them a 2:1 syrup and spiked it with some Honey-B-Healthy as a stimulant. I put that in their hive-top feeder yesterday and they were very interested. Do I keep doing this all winter? I imagine that their heat will keep it thawed and we can be very quick about refilling it, so their exposure will be minimal, but I worry about their health. I've been hearing about various bee cakes or patties to make with pollen, but I haven't found a reputable recipe or a scenario that will apply to my need for Winter-long feeding.

Do you have a recipe for me? If so, how often should I add a cake? Should I keep the syrup too? Does the cake go on top of the frames and under the hive-top feeder? Are there other supplements they will need since they are not getting their own honey? How do I save my girls?