2. Place a saucer with five metal teaspoons in a flat place in your freezer for testing the jam later. Rinse the rosemary well under cold water, pat it dry between two clean kitchen towels, and set aside.
3. Remove the pears from the refrigerator and transfer them to an 11- or 12-quart copper preserving pan or a wide nonreactive kettle, stirring well. Position a food mill over the storage container that held the pears and set aside.
4. Bring the pears to a boil over high heat, stirring every 2 minutes or so. Cook, stirring frequently with a heatproof rubber spatula, until the mixture starts to thicken and the pear pieces are semitranslucent, 15 to 20 minutes. Remove from the heat and transfer one-third of the mixture to the food mill. Put as much fruit as possible through the mill, then scrape any solids that will not go through back into the jam mixture. Return the pureed fruit to the jam kettle, breaking up the chunks as you go. Place the jam over medium-high heat and continue to cook, stirring gently and constantly, until the jam has thickened and no longer appears watery, about15 minutes more.
5. When the jam seems ready, test it for doneness. To test, carefully transfer a small representative half-spoonful of jam to one of your frozen spoons. Replace the spoon in the freezer for 3 to 4 minutes, then remove and carefully feel the underside of the spoon. It should be neither warm nor cold; if still warm, return it to the freezer for a moment. Tilt the spoon vertically to see how quickly the jam runs; if it runs slowly, and if it has thickened to a gloppy consistency, it is done. If it runs very quickly or appears watery, cook it for another few minutes, stirring, and test again as needed. While you are waiting for the jam in the freezer to cool, skim off any white foam that appears on the surface of the jam in the pan.
6. When the cooking is completed, place the rosemary into the mixture and let steep for a few minutes off the heat. Stir and carefully taste the jam and either remove the sprigs or leave them for another minute or two, keeping in mind that their flavor will be slightly weaker once the jam has cooled. Using tongs, discard the rosemary. Add a generous drizzle of pinecone bud syrup and stir well. Pour the jam into sterilized jars and process according to the manufacturer's instructions.
Andrea Reusing is the creator of the restaurant Lantern in Chapel Hill, N.C., and author of the book Cooking in the Moment: A Year of Seasonal Recipes. In this installment of The Key 3, she shares with Lynne Rossetto Kasper the techniques behind three of her favorite recipes: Turnip Soup, Overnight Braised Short Ribs and Tomato Salad.