Trim off any leftover stems, rinse away debris, and wash the figs thoroughly. Cut them into halves or quarters if they're on the larger side. Remove any that look off, cracked or split.
Add the figs to a large saucepan or pot over medium-high heat. Zest and juice the orange straight into the pot, along with the rosemary sprig.
Bring to a boil, then lower the heat and simmer, stirring frequently to prevent sticking. Cook roughly an hour (at least) until reduced by half and thick and glossy. Remove the rosemary, taste, and stir in honey if you'd like it sweeter, letting it melt in off the heat.
For canning, add citric acid now, ¼ tsp per pint (473 ml) or ½ tsp per quart (946 ml). Bottled lemon juice is an alternative: 1 tbsp per pint or 2 tbsp per quart, though it will shift the flavor toward lemon rather than letting the figs lead.
Sterilize jars and lids, either boiled fully submerged for a few minutes or baked at 100°C (212°F) for ten. Reheat the jam to boiling if it's cooled, then fill jars while hot, removing air bubbles, wiping rims, and sealing tightly.
Process in a boiling water bath, fully submerged, for 10 minutes (longer at higher altitude). This step is essential for shelf stability, don't skip it.
Remove jars and let them cool undisturbed, wrapped in a blanket overnight. Check seals the next day, press each lid center. Unsealed jars go in the fridge.
If you're not canning the fig jam, skip the citric acid too, fill clean, sterilized jars, remove air, and refrigerate. Good for several weeks.