Make the brine. Combine the vinegar, brown sugar, water, kosher salt, mustard seeds, celery seeds, and turmeric in a saucepan over medium heat. Bring the mixture to a simmer, stirring occasionally, until the sugar completely dissolves. Once simmering, cook for about one minute. Remove from heat and let cool.
Prep the jars. While the brine is cooling, tightly pack the sliced cucumbers into four pint-sized jars. Ensure the cucumbers are compacted well to leave room for enough brine to cover.
Cover cucumbers with brine. Once the brine has cooled, pour it over the cucumbers in the jars, making sure they are completely submerged. Adjust the cucumbers as needed to ensure no air pockets and cucumbers are fully covered.
Store. Seal the jars tightly and refrigerate. For best flavor development, let the pickles marinate for at least 24 hours before consuming. These pickles can be stored in the refrigerator for up to 3 months.