Pour vinegar, water, salt, sugar, and mustard seeds into a sauce pan. Heat over medium-high heat until the mixture boils.
As soon as it boils, stir the mixture gently and turn off the heat. Allow the mixture to cool slightly on the stove while you prep the veggies.
Chop the cauliflower head into small florets, slice the carrots and celery on a diagonal into slices, slice the bell pepper and jalapeño (if desired). Arrange the veggies in three 2 cup wide mouth jars.
Spoon the mustard seeds from the brine into each jar. Pour the slightly warm brine over the veggies.
Allow them to cool completely at room temperature. Then, place the lid on the jars and place in the fridge. They will continue to pickle in the fridge so let them sit for at least 24 hours before consuming.
Notes
I like to use a 2 cup wide mouth canning jar to store this giardiniera recipe. Personally, I don't like to use narrow mouth jars because it can be harder to arrange the raw chopped veggies properly.
In place of jalapeños you can use a pinch of red pepper flakes. You can also add things like bay leaves, fennel seeds and black peppercorns to the brining liquid to alter the flavor of this giardiniera recipe.
Finely minced giardiniera is a very popular topping for hot dogs and sandwiches. If you want to serve this on a hot dog or sandwich, chop it up into smaller pieces before serving.