Slice cucumbers into thin discs. Cut onions in half, then slice them into strips. Slice green and red bell peppers into strips.
Combine sliced cucumbers, sliced onions, and peppers in a large bowl, tossing to evenly distribute the vegetables so they are mixed together. Sprinkle with the coarse salt, then toss to evenly distribute the salt. Cover with a layer of ice about an inch or two thick.
Transfer the bowl to the fridge and let the vegetables sit for 3 hours, then discard the ice. Rinse the vegetables thoroughly with cold water and drain well.
Combine sugar, vinegar, garlic, celery seed, mustard seed, and turmeric in a large pan over medium heat. Bring to a boil.
Add the cucumber and onion mixture and heat just until it starts to boil again. Don't overcook - the cucumbers should still be crisp.
Transfer the cucumbers and onions to clean, sterilized jars while still boiling hot. Fill to within about 1 inch of the brim, then pour some of the pickling liquid over the vegetables until the jar is filled about ½ inch from the brim.
Make sure the rim is clean by wiping it with a clean towel so it will seal properly. Place a clean lid on each jar and secure it with the metal rings.
Arrange the jars in a large canning pot filled with hot water. The water should cover the jars by a full inch. Bring to a boil for 15 minutes to seal. Carefully remove each hot jar from the water using tongs or a jar lifter.
Let the jars cool completely to room temperature. They should make a popping sound as their lids seal. If any of the jars don't seal properly, store them in the refrigerator.