Pour the water, vinegar, salt and spices into a small saucepan. As it comes to a boil, pack your veggies into a freshly washed jar (one pound of trimmed and quartered carrots fits nearly perfectly into a wide-mouth quart-sized jar). You can also tuck a slice of lemon, a hot pepper or a garlic clove into the jar as well.
When the brine is boiling, pour it into the veggie-packed jar, leaving about 1/2 inch of headspace. Make sure to run a butter knife around inside the jar, to release any air bubbles trapped behind the vegetables (this isn’t as important in this case as it is when you’re doing a hot water bath, but it’s a good habit to get into anyway).
Gently screw a two-part canning lid on the jar (making sure to protect your hands with a towel or potholder) and let it sit until it’s cooled down. The lid may seal during the cooling process. However, this does not mean it’s safe to store it at room temperature indefinitely. Once the jar is fairly cool, it should still go in the fridge. Let them chill out in the brine for at least 2-3 days before you dig in.