Scrub turmeric and ginger thoroughly. Slice thinly to release flavor evenly.
Add turmeric, ginger, and 3 cups of water to a saucepan. Bring to a boil, then reduce to a gentle simmer.
Simmer for 15 to 20 minutes until the liquid turns deep golden and aromatic.
Let the mixture cool slightly, then transfer to a blender. Add remaining water, tamarind, black pepper, and salt.
Blend until completely smooth.
Strain the mixture through a fine mesh sieve or nut milk bag into a jug. Press gently to extract liquid.
Stir in fresh citrus juice and sweetener to taste.
Chill for 1 to 2 hours before serving. Shake well before pouring.