In a small saucepan, combine the filtered water, rice vinegar, granulated sugar, and kosher salt. Place over medium heat and stir gently until the sugar and salt completely dissolve. Do not let it boil. Remove from heat and let it cool completely to room temperature.

Peel the carrots and cut them into hearty, 2-inch matchsticks. Slice the cucumber into uniform rounds, keeping the peels partially intact. Thinly slice the white onion into half-moons and slice the red chili into thin rounds.

In a clean, rustic glass jar, tightly alternate layers of the carrots, cucumbers, and white onions. Tuck the red chili slices against the glass so they are visible. Leave about 1 inch of headspace at the top of the jar.

Once the pickling liquid is at room temperature, pour it into the jar over the vegetables, ensuring everything is fully submerged. Tap the jar to remove air bubbles, seal tightly, and refrigerate for at least 24 hours before serving.