Special equipment: lollipop collar molds, candy thermometer
Line lollipop collar molds with cinnamon sticks and lay on a silpat or greased cookie sheet. Combine all of the ingredients, except the coffee extract, in a clean, dry small saucepan fitted with a candy thermometer and bring to a boil over high heat. Without stirring, cook until the mixture reaches 305 degrees or "hard crack" stage on the candy thermometer. (While the syrup is cooking, occasionally wash down the sides of the pan with a clean brush dipped in water, to prevent crystallization.) Half-fill a large bowl with ice water. When the mixture is done, remove the pot from the heat and dip it into the ice bath for 15 seconds to stop the cooking. Remove the pot from the ice bath and swirl in the coffee extract. To avoid air bubbles in the finished lollipops, stir the mixture gently in both directions, and be careful not to over mix. Pour the syrup into the molds, filling them 2/3 full or just pour the slightly cooled (so it's a little thickened) syrup in coin shapes at the ends of the cinnamon sticks. Cool at least 20 minutes, until hard. Remove from molds or from silpat. Store in an airtight container.