Cut 6 slits in the skin lengthwise in each kumquat with the tip of a sharp paring knife, making sure not to cut all the way though, and keeping the top and bottom of the kumquat intact.
Pinch the top and bottom of each kumquat to open the slits and pop out any large seeds using the tip of your paring knife. It's okay if you don't get all the seeds, some of them will slip out during cooking; you can also squeeze them out after cooking.
Bring a large pot of water to a boil. Add sliced kumquats, bring water back up to a boil, immediately remove from heat, drain kumquats, and give them a light rinse. This step removes natural wax from the skins and any rogue seeds you may have missed.
Heat 2 cups water and 1½- 2 cups sugar in a pot over medium heat, stirring until sugar dissolves.
Add sliced kumquats and any spices (ginger, cinnamon stick, etc) if using, and turn up heat to medium-high. As soon as it starts to boil, reduce heat and simmer until the skins look glassy and translucent, about 45 minutes.
Remove Candied Kumquats from heat. Allow to cool slightly, then pour off the liquid into a glass jar for another use (like cocktails, tea, or salad dressing!).
On a flat surface like a cutting board, flatten each kumquat into a flower shape. Any rogue seeds will squish out through the cuts and you can discard those. Place the kumquat flowers in a single layer on on a parchment-lined baking sheet. Dry out the Candied Kumquat flowers in the oven at the lowest temperature 200°F or lower (mine goes down to 170°F), at least 3 hours, and up to 6 hours. The Candied Kumquat Flowers will not harden.
Store Candied Kumquat Flowers in an airtight container in the refrigerator for up to 1 week.