In a saucepan, combine 1 cup water with the vinegar, sugar, salt, bay leaves, and pink peppercorns. Bring to a boil over medium-high heat, immediately turn the heat to low, and let simmer until the sugar is dissolved, about 5 minutes. Meanwhile, in a 2 quart-size mason jar, combine the peaches, fennel, onion, and fennel flowers.

Carefully pour the pickling liquid into the mason jar. Press the contents down with a wooden spoon without bruising the ingredients to make sure they are covered with the pickling liquid. Let the jar sit at room temperature for at least 30 minutes or up to 1 hour, then use or refrigerate, sealed, for up to 1 week.