Place 2 boneless, skinless chicken breasts in a large saucepan and add enough water to cover by about 2 inches. Add 1 teaspoon of the kosher salt, and bring to a boil over high heat. Reduce the heat to low and simmer until the chicken is cooked through and registers at least 165ºF in the thickest part, 8 to 10 minutes.

Transfer the chicken to a cutting board. Let cool for about 5 minutes. Meanwhile, dice 2 Persian cucumbers or 1 large English cucumber (about 3 cups). (No need to peel first or remove the seeds, but feel free to do so if you prefer.) Place the remaining 1 teaspoon kosher salt, 1/4 cup rice vinegar, 1 tablespoon toasted sesame seeds, 1 teaspoon coarsely ground black pepper, 1 teaspoon granulated sugar, and 1/2 teaspoon toasted sesame oil in a large bowl and whisk until the sugar and salt are dissolved.

Dice or shred the chicken into bite-size pieces. Add the chicken and cucumbers to the dressing and toss to combine. Taste and season with more kosher salt as needed. Garnish with chopped scallions or fresh cilantro if desired.