Wash the cauliflower, carrots, cucumbers, red bell pepper, and green beans thoroughly under cold water. Cut the cauliflower into small florets, slice the carrots into thin rounds, and chop the cucumbers and bell pepper into strips. Trim the green beans to your preferred length. Place all the prepared vegetables in a large mixing bowl.

In a medium saucepan, combine vinegar, water, kosher salt, sugar, mustard seeds, and black peppercorns. Heat over medium-high heat until it reaches a gentle boil, stirring occasionally until salt and sugar are dissolved.

Carefully pour the hot pickling liquid over the prepared vegetables in the mixing bowl, ensuring it covers them completely. Use a wooden spoon to gently press the vegetables down to release air bubbles.

Allow the mixture to cool to room temperature, about 20-30 minutes, ensuring the brine isn't steaming hot.

Transfer the cooled vegetables and brine into clean, airtight jars. Seal tightly and refrigerate for at least 24 hours before enjoying.