Place the figs in the food processor and pulse about 10 times or until the figs are minced into very small pieces.
Place the minced figs, lemon zest, lemon juice, rosemary sprigs, honey, sugar, and water in a large saucepan. Bring the mixture to a boil, stirring well to dissolve the sugar and honey. Reduce the heat to medium-low and let the jam simmer for about 15 minutes or until it is thick. Stir the jam frequently so it doesn't stick or burn.
Remove the rosemary sprigs and ladle the jam into small 4-8 ounce jars. Place the lid on top of each jar and let them cool.
Refrigerate the jam for up to four weeks, or freeze it for up to six months.
Notes
This recipe makes about two cups. The nutrition information is based on a 1/4 cup serving size.