Rinse okra in a colander. Add 3 tablespoons salt, and toss to combine. Let okra drain in sink 10 minutes. Meanwhile, prepare an ice-water bath; set aside.
Put remaining 3 tablespoons salt, 2 cups water, the vinegar, sugar, bay leaves, pickling spice, cayenne, onions, and jalapeno into a nonreactive medium saucepan. Bring to a boil over medium heat, stirring until sugar has dissolved.
Rinse okra under cold running water to remove salt. Transfer to a large nonreactive bowl. Pour brine over okra. Set bowl in ice-water bath; let cool 10 minutes. Transfer bowl to refrigerator to cool completely, about 25 minutes. Serve.