Combine the 120g of light brown sugar and 240ml of water in a medium saucepan over low to medium-low heat. Stir until the sugar is completely dissolved and the liquid is warm and clear. Add the single cinnamon stick, the skin-on apple cubes, and the cranberries together. Bring the combined mixture just to the lightest possible simmer — bubbles appearing at the edges rather than a rolling boil — then reduce immediately to the lowest sustainable heat. Cook for 8–10 minutes. The cranberry's behaviour is the visual timer: cranberries begin bursting between 5–7 minutes, releasing their vivid magenta-red juice into the surrounding syrup and producing an immediate, dramatic colour shift. The apple's skin releases its aromatic compounds more slowly — the warm, characteristically crisp apple fragrance becomes specifically present at 8–10 minutes. The cinnamon's single-stick cinnamaldehyde extraction progresses throughout the cooking period: at 5 minutes it is subtle; at 8–10 minutes it is warm and specifically present without dominating; beyond 15 minutes it would be assertive. The light brown sugar's molasses-adjacent warmth specifically amplifies both apple's warm ester character and cinnamon's cinnamaldehyde depth. The result is a specifically more complex, more layered warm-spiced apple-cranberry syrup than white sugar's neutral sweetness provides. Remove from the heat. Discard the cinnamon stick before straining — unlike herbs and zests that are removed from the liquid, the cinnamon stick continuing to sit in the warm strained syrup as it cools would continue extracting. Remove it from the pan along with the fruit solids during straining. Strain through a fine-mesh sieve, pressing gently but firmly on the cooked apple and cranberry solids. The cranberry's burst flesh releases readily under moderate pressing; the apple's cooked flesh is softer than raw but requires deliberate pressure. Press until the solids are visibly drier — the yield is a vivid, specifically deep cranberry-red syrup with warm apple and cinnamon aromatic depth. Allow to cool completely.

Pour the cooled apple cranberry syrup into the large pitcher. Add the 500ml of cloudy apple juice if using. Add 2 litres of ice-cold water and the optional salt. Stir gently until fully combined. The cloudy apple juice's role is body provision rather than flavour contribution: the syrup's extraction at 300g of apples in 240ml of water produces a flavourful but relatively low-volume syrup component; the 500ml of cloudy apple juice specifically adds the apple-character liquid volume and body that makes the finished pitcher taste specifically of apple rather than specifically of a light apple-cranberry-flavoured water. Without the apple juice, the total fruit-character liquid from the syrup is approximately 200–250ml in 2.3+ litres of water — producing the diluted, flat result the note describes as "not restraint; that's dilution." Taste with the apple-cranberry crowd assessment: the drink should be specifically crisp and cool-adjacent in character, the apple's warm-fruity aromatic freshness clearly present, the cranberry's tartness providing the structural brightness that keeps the cinnamon's warmth from making the drink feel specifically heavy or warm-season. The balance is specifically autumn-light rather than mulled-beverage. If the cinnamon is too assertive despite the single stick — the cooking temperature was too high or the sieve pressing was too firm with the cinnamon stick still in the pan; more cold water dilutes it. If the drink tastes flat — the salt corrects this without adding any perceptible flavour.

Cover and refrigerate for 1–2 hours. The cold rest specifically repositions the apple-cranberry-cinnamon combination away from any warm-beverage association and into the specifically refreshing register. Stir once before the first pour. Prepare apple slices immediately before service. Garnish with fresh cranberries for the visual contrast of vivid red in the amber-cranberry drink. Serve cold over ice.