In a small saucepan, combine the sliced apples, sugar, and water. Bring to a gentle simmer over medium heat and cook for 8–10 minutes, stirring occasionally, just until the apples soften and release aroma. Do not reduce or caramelize — this is extraction, not cooking.
Remove the saucepan from heat. Add the grated ginger and let steep for 3–4 minutes only, just until a clean ginger bite develops. Ginger should be sharp and fresh, never hot or muddy.
Strain through a fine-mesh sieve into a bowl or measuring jug. Do not press the solids. Discard the apple and ginger. Stir in the pinch of fine sea salt and let the syrup cool completely.
In a pitcher, combine 120–140 ml of the cooled apple ginger syrup with plenty of ice. Pour in the chilled club soda and stir gently once or twice to integrate without killing carbonation.
Pour into ice-filled glasses and garnish with thin Fuji apple slices and fresh ginger slices.
