Combine the chopped ginger and turmeric in a medium saucepan with the filtered water. Bring to a boil over high heat, then reduce the heat to low and simmer for 20 minutes until the water is deeply golden and fragrant.
Remove the saucepan from the heat and let the mixture cool for 10 minutes until it’s safe to handle.
Strain the liquid through a fine-mesh sieve or cheesecloth into a large bowl or pitcher, pressing on the solids to extract as much liquid as possible. Discard the solids.
Stir in the lemon juice, honey, and black pepper until the honey is fully dissolved and the mixture is well combined.
Pour the liquid into a clean glass bottle or jar with a tight-fitting lid. Store in the refrigerator for up to 1 week.
Shake well before each use and serve chilled. A typical serving is 2 fluid ounces per shot.