Combine cranberries, apple, shallot, brown sugar, cider, vinegar and salt in a small saucepan. Bring to a simmer over medium heat.
Reduce heat to medium-low and cook for 15 to 18 minutes, stirring occasionally, until the berries burst, apple pieces soften and the chutney holds a soft mound on a spoon.
Transfer chutney to a shallow container and refrigerate promptly for about 60 minutes until cold; chilling is included in preparation.
Lay Havarti over the croissant bottoms and fold 3 ounces turkey loosely over each portion of cheese.
Divide cold chutney over the turkey, leaving any loose liquid in the container, and add a loose portion of dry watercress.
Close with the croissant tops and serve cold or refrigerate at 40°F or below until serving.