Peel the cucumbers if the skins are thick or waxed, and cut them into 2- or 3-inch spears or crosswise into rounds about 1/2 inch thick.
Put the sesame seeds in a large nonreactive pot over medium-high heat. Cook, shaking the pot nearly constantly, until they’re fragrant and begin to darken a little, 1 or 2 minutes. remove them from the pot.
add the vinegar, garlic, syrup, red chile flakes, and salt to the pot along with 2 cups water, and bring to a boil. Put the cucumbers and sesame seeds in the pot and remove from the heat. let the vegetables sit in the brine for 30 minutes, stirring once or twice to make sure they’re all covered at least part of the time. transfer to jars or other airtight containers and refrigerate for up to a week.