Melt butter in a saucepan over medium heat until it begins to bubble, about 1 minute. Add sugar and molasses; stir until sugar has absorbed molasses and butter, about 3 minutes. The mixture will be very dry. Add 2 cups apple cider. Mix well and bring to a slow boil. Add cinnamon stick and continue to simmer syrup for about 10 minutes.

Whisk together 1 tablespoon apple cider, lemon juice, and cornstarch in a small bowl.

Pour cornstarch mixture into syrup in the saucepan, whisking continuously until fully incorporated. Simmer until thickened, with a consistency similar to warm maple syrup, about 5 minutes. The syrup will thicken upon cooling.

Serve warm. Store leftovers in an airtight container in the refrigerator for up to 3 weeks.