Prepare the Vegetables: Slice the cucumbers and carrots into sticks, about 2-3 inches long. Boil the potato until tender, peel, and slice into rounds. Thinly slice the onion. Place all the prepared vegetables in a large, clean jar or container that can be sealed.
Make the Pickling Brine: In a medium saucepan, mix together the vinegar, water, sugar, and salt. Incorporate the mustard seeds, fennel seeds (if desired), coriander seeds, turmeric powder, black peppercorns, bay leaves, red pepper flakes (if included), and sliced garlic. Heat the mixture over medium heat, stirring occasionally, until it reaches a boil and the sugar and salt have fully dissolved.
Pour the Brine Over the Vegetables: Once the pickling brine has come to a boil and the sugar and salt are dissolved, remove it from the heat. Carefully pour the hot brine over the prepared vegetables in the jar, making sure all the vegetables are submerged.
Pickling and Storing: Once cooled, seal the jar or container and refrigerate the pickle for at least 24 hours to let the flavors develop. For best results, let it sit for 2-3 days before serving.
Serve: Serve this tangy vegetable pickle alongside your favorite sandwiches, grilled meats, or as a zesty side to any meal.