In a large mixing bowl add the cucumbers, salt, and sugar and toss to combine. Allow to cure for 15 to 20 minutes and then strain but do not rinse.
Meanwhile, in a food processor combine the gochugaru, minced garlic, fresh ginger, Asian pear, fish sauce, and honey and pulse thoroughly until paste like. Add the chili paste to the strained cucumbers along with the carrots and garlic chives and mix well until everything is thoroughly coated.
Pack the cucumber mixture into a glass jar and tamp down with the back of large spoon or ladle until the mixture is covered in its own released juices. Serve immediately or secure a paper towel around the lid of the jar with a rubber band or clean hair tie and leave the kimchi out at room temperature to ferment for 12 to 24 hours before refrigerating. Enjoy as desired.