Add the cucumbers, onion and banana peppers to a clean glass quart jar.
Add the vinegars, honey, salt, garlic, mustard seeds, peppercorns, turmeric, chile flakes and bay leaves to a saucepan and bring to a boil, stirring to dissolve the honey and the salt.
Carefully pour the brine over the pickles, stopping 1/2 inch from the top. Let cool completely, then cover with a lid and refrigerate. The pickles will be ready to eat in a few hours but taste best after chilling overnight. Pickles will keep in the refrigerator for up to 1 month.