Just made an experimental batch of chocolate braggot. About 60% various grain and 40% honey, OG 1.069, Safale S-04 yeast. We like to have some sweetness as well as mid-high carbonation in the final results hence wondering if there's a safe way to backsweet it (preferably with honey, not non-fermentables like lactose) yet keep the fizzy part of it? Controlled pasteurisation perhaps?
It's worth mentioning that it depends somewhat on how you plan to package the braggot.
If you're planning to bottle condition, I'm not sure it's possible to back-sweeten with something fermentable like honey and still allow yeast to do the carbonation. You might still be able to bottle if you keg/force-carbonate and then use a beer gun or something similar. If you're just planning to keg, life is easier.
As for back-sweetening itself, this page describes the primary method I know for how to accomplish this: adding potassium sorbate to inhibit future yeast activity and then later adding the honey. This will allow you to safely back-sweeten without having to filter out or kill the yeast.
Potassium/sodium metabisulfite (e.g. Campden tablets) may also work. This page seems to recommend using it in conjunction with potassium sorbate. Both are pretty widely used and I'm sure you can find a lot of dosage and health information on both with a couple quick searches.
Keeping things cold may help but, as mentioned, you would still want to consume it relatively quickly as some fermentation may still occur. Pasteurization and filtering are also potentially options but in order to do them with confidence that no fermentation will happen could be difficult, which I think is while many go the route of chemically inhibiting/killing the yeast.
Typically you would try to mash in the high alpha-amylase range to insure some unfermentables or use some dextrin malts.
If the beer is finished and needs backsweetened you can add more honey but this will require the beer to be kept cold and consumed quickly or using a chemical yeast inhibitor to prevent further fermentation. Or adding an unfermentable sugar.