Harvesting frozen herbs, pruning frozen plants

We just had a hard freeze and all my basil froze with good leaves on it. Can I do anything with the frozen product or should I just compost it? Also, are the seeds more or less viable now? Also... is it wise to prune the plants back to the ground to keep those "carbon pathways" in the soil and let it decay that way? Or is that asking for disease? ...Thanks in advance.

P.S. isn't Borage supposed to be cold-hardy? One of mine froze... but I guess it may have been because it was a leggy one?

Many herb leaves will deteriorate once frozen. However, it is quite common for people to make pesto while the plants are prolific, and freeze the pesto for a fresh treat once the annuals season is gone.

Generally speaking, 'hardy' means a bit different when speaking of annuals.
When speaking of perennials, hardy means that they will survive the winter.
With annuals, it just means that you can put them out earlier than the non-hardy types (and also leave them longer).

Most herbal plants are less affected by diseases than fruiting annuals.
I see no problem chopping them at the ground. As long as your soil microbes are active, they will have food, and keep working for you. Roots decaying deep within your soil is one of the best ways to improve your soil. If you top your garden with a good layer of mulch/compost, this will help keep the soil warmer for longer. This keeps your microbes active longer.

Thank you John. This was very helpful. Is it the same making a product from basil leaves that were frozen on the plant rather than in the freezer?

What about the seeds that froze outside on the plant? Are they more or less viable? I know some seeds like to go through a freeze... but is this true for basil?

The seeds should be viable and you can sew them in the spring. Basil is an annual unless you are in zone 10 where the temperature hardly ever dips below 40F. If you caught it frozen and kept the leaves in the freezer, you might be able to still use them in cooking, but if the leaves thawed out I'd throw them in the compost heap. The freeze killed them, and once they thaw, they are going to be decomposing, losing flavor by the minute.