The end result was delicious, but took a long time to get to. The thing about cordials is that they are addicting. You set them to infusing and then you have to wait for weeks or months to appreciate them. My natural impulse was to make more and experiment in the mean time. Thus our first creations, Chitters and Persephone were born.

Seeds from 3.5 pomegranates, mashed
10 thin-ish slices of ginger
1.75 liters vodka
sit with stirring for 10 days
filter, once coarse, twice fine
add cooled simple syrup (4 cups water, 2 cups sugar)
mellow 1 week
fine filter into bottles

1 cinnamon stick
80 hazelnuts, chopped
20 cloves, smashed
10 allspice berries, smashed
1.5 nutmegs (is this a word?), chopped
1.75 liters vodka, brita filtered
0.25 liters brandy
sit with shaking for 3 weeks
filter twice, one coarse, one fine
add cooled simple syrup (4 cups water, 2 cups sugar)
mellow 1 week
fine filter into bottles
Notes: Ideally you would use a 70% grain alcohol like Everclear, which has no flavor, but brita filtering (we did it 5 times) cheap vodka does improve the flavor some.
Infusing for longer isn't always better. Fruits get mushy and hard to filter out, the pomegranate definitely didn't need more than 10 days.
Letting the simple syrup cool before you add it means that it will stay clear in solution, apparently when it is added warm cloudiness can form.
The most time consuming part of the project is actually filtering everything through coffee filters to get out all of the particles. We weren't patient enough with the Persephone, and a bit has fallen out since it was bottled. That one was our least favorite; the ginger flavor was surprisingly subtle and I think we'll add more next time. The Chitters, the ingredients of which were inspired by Italian nut liquors and the name coming from everyone's favorite squirrel, turned out excellent. Though I would probably put in less cloves, allspice and nutmeg in the future.
If you are interested in cordial making, you'll need some supplies:
2 liter, well sealed glass jars
a mortar and pestle
a nut grinder (we love the nut grinder!)
a microplane zester
lots of funnels
a stand alone coffee filter
paper coffee filters
lots of bottles (I like the flip-top kind, so I buy things in those bottles and save them, but this place has some great ones: http://www.specialtybottle.com/)