Make the pickling liquid: Place 1 cup water in a medium nonreactive saucepan along with vinegar, sugar, bay leaves, and mustard seeds. Bring to a simmer over medium-low heat, stirring occasionally to dissolve sugar.
Pickle the vegetables: Place any one of the suggested vegetables in a heatproof nonreactive container and add pickling liquid. Cover and let cool to room temperature. Transfer to refrigerator and chill before serving. Pickled vegetables can be kept refrigerated, completely submerged in their liquid, in an airtight container, for up to 2 months.