Combine the filtered water, vinegar, mineral salt, dill, and optional garlic in a small stainless-steel saucepan. Bring the brine to a full boil, with active bubbles across the surface.
Pack the peeled 1/4-inch cucumber slices snugly into the prepared jar or jars without crushing them. Pour or ladle the hot brine over the slices, including the chosen dill branch and optional garlic, until every cucumber layer is wet.
Leave the jar or jars uncovered until both the glass and brine cool fully to room temperature.
Cover each fully cooled jar and refrigerate until chilled. Eat the pickles once chilled, or refrigerate them for 24 to 48 hours for deeper pickle flavor and the preferred texture.