Wash and trim the cucumbers, then slice them into thin, even rounds. Keep them firm rather than paper-thin so they stay crisp after soaking in the brine.

Combine vinegar, water, sugar, salt, mustard seeds, celery seeds, black pepper, and red pepper flakes in a saucepan. Warm over medium heat until the sugar and salt dissolve.

Stir the sliced garlic and jalapeño into the warm brine. Let them heat briefly to release their flavor and add a pleasant spicy kick.

Place the cucumber slices in a clean glass jar or airtight container. Slowly pour the warm brine over them, making sure the cucumbers are well covered.

Let the jar cool at room temperature before covering it tightly. This keeps the pickles from becoming too soft and makes refrigeration easier.

Refrigerate the pickles for at least 4 hours, although overnight gives the best flavor. The longer they chill, the more the sweet, tangy, garlicky, and spicy flavors develop.