Wash parsnips and carrots well. Remove tops and cut lengthwise into small sticks. Cutting the sticks tall enough to fill jar 1-1.5in below the rim is helpful for even packing.
Place grated ginger and red pepper flakes in the bottom of a quart sized jar. Place parsnip and carrot sticks atop ginger and pepper flakes, trying to line them up and pack them in as evenly as possible. Leave 1 inch of head space at the top of the jar.
Make a brine of 2 cups water to 2 Tbsp of sea salt. Stir to dissolve salt as well as possible and pour over vegetables, leaving 1 inch of head space. Add more water, as needed. There is no need to add more salt.
Plae the lid on the jar and add the airlock, if using. Allow to ferment at room temperature for 5-10 days. If you are not using an airlock, be sure to burp the jars daily to release pent-up gases.
Once the initial fermentation period is over, and the carrots and parsnips are tangy enough to your taste, move them into cold storage.