Prepare the figs: Trim the stems from the figs and quarter them. If the figs are particularly large, cut them into smaller pieces so they cook at a similar rate. There is no need to peel ripe figs.

Combine the ingredients: Place the figs, sugar, lemon juice, water, lemon zest, and kosher salt in a heavy-bottomed 3-quart saucepan. Stir gently until the figs are evenly coated with the sugar mixture.

Let the fruit macerate: Cover the saucepan and let the figs stand at room temperature for 30 minutes. This allows the sugar to begin drawing moisture from the fruit and reduces the amount of liquid needed during cooking.

Bring the mixture to a simmer: Place the saucepan over medium heat. Stir occasionally until the sugar has dissolved and the liquid begins to simmer. Once bubbling, reduce the heat to medium-low.

Cook the figs gently: Simmer uncovered for about 35 to 45 minutes, stirring every few minutes to prevent sticking. The figs should become tender and glossy while the syrup gradually thickens.

Watch the syrup carefully: Toward the end of cooking, stir more frequently. The preserve is ready when the syrup coats a spoon and slowly runs off rather than flowing like water. Do not cook until it looks completely dry; it will thicken considerably as it cools.

Check the consistency: For a quick test, place a small spoonful on a chilled plate and let it sit for 30 seconds. Tilt the plate. The preserve should move slowly and remain somewhat mound-like rather than running freely. If it is very thin, continue cooking for another 3 to 5 minutes and test again.

Cool the preserves: Remove the saucepan from the heat and let the preserves cool for about 30 minutes. Transfer to clean containers, leaving the preserves uncovered until they have cooled enough to avoid trapping excess condensation.

Chill and set: Cover the containers and refrigerate the preserves for at least 12 hours. The syrup will become thicker and more jam-like as it chills.

Serve: Bring the desired amount to room temperature for easier spreading, or serve chilled. Spoon the preserves over toast, biscuits, yogurt, oatmeal, or cheese as desired.