Bring your white wine vinegar and water up to a boil in a medium saucepan over medium-high heat. Add your kosher salt, sugar, and 3 bay leaves. 

While waiting for your vinegar/water to reach boiling, cut your half head of cauliflower into small bite-sized pieces, discarding most of the stalks. Peel and chop carrots into small-sized pieces. 

Add both the cauliflower and carrots to the boiling liquid and reduce heat to a simmer and cook for 3 minutes. 

While simmering, chop celery and red bell pepper into similarly sized pieces as the cauliflower and carrots. 

After 3 minutes, add celery and red bell pepper and simmer for another 2 minutes. 

Remove the pot from the heat. Fish out and remove all three bay leaves.

Chop your green olives, pepperoncinis, and pickled jalapeno (if using) into small bite-sized pieces and add all three vegetables to the now cooling pot with the cauliflower, carrots, celery, and red pepper. 

In a large mixing bowl, pour 1/3 cup olive oil, 2 teaspoons fennel seeds, and 1 teaspoon dried oregano. This is your marinade for the giardiniera. Whisk to combine. 

Using a colander or strainer, drain the vegetables. Add drained vegetables into the marinade and stir to combine. 

Let vegetables marinate tossing occasionally until they are cooled. This may take 20 or 30 minutes. 

Add cooled vegetables and marinade to your containers (I use pint-sized Ball/Mason jars). Since I usually have multiple jars to fill. I make sure to attempt to get an equal amount of marinade in each container. If your marinade only comes up about a third of the jar, you should add a bit more olive oil to each jar. You want the oil/marinade to be at least three-quarters of the way up to the level of the vegetables. 

Refrigerate and enjoy after at least one day in the marinade. You should stir the giardiniera before serving to make sure each spoonful is coated again in the marinade.