Add ginger, lime zest, spices, bitters, and rum to a plastic pouch.

Vacuum seal and cook in an immersion circulator at 160F for 2 hours.

Separate solids and rum mixture.

Add solids, sugar, and water to a large saucepan on medium heat.

Simmer for 1 hour.

Strain, add reserved rum mixture and orgeat syrup, and store in the refrigerator.