Place cucumbers in a bowl; sprinkle with 1 teaspoon of salt.
Fill a pot with water; add remaining 1/2 teaspoon salt, chicken, cinnamon, peppercorns, cloves, cardamom, and bay leaf. Bring to a boil; cook until chicken is no longer pink in the center and an instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C), about 35 minutes.
Transfer chicken to a cutting board; cool until easily handled, about 15 minutes. Remove skin and bone; cut chicken into small pieces. Transfer to a bowl.
Stir mayonnaise, light mayonnaise, and garlic into the cucumbers. Pour over chicken and mix until combined.