In a large measuring cup, add the tahini, Dijon mustard, lemon juice, apple cider, salt, pepper, and brown sugar. Stir until smooth.
If the mixture feels very thick, add 1 tablespoon of ice-cold water to loosen it slightly. If it looks pourable, hold off on adding more water for now.
Slowly stream in the olive oil with one hand while whisking with the other. The dressing will thicken as it emulsifies. After that, decide if you need more water to thin it.
For reference, I started with 1 tablespoon of water, then added 2 more tablespoons to make the dressing pourable but still creamy.
Add the chopped fresh dill and stir to incorporate. Taste and adjust with more salt, if needed.
Notes
Apple cider substitute: Use unsweetened apple juice. Do not use apple cider vinegar.
Can I use dried dill? Fresh dill gives the dressing a brighter, cleaner flavor. You can use dried dill, but the flavor will be softer and less distinct. Start with ¾ teaspoon, then add up to 1 teaspoon if needed.
How much water should I add to thin the dressing? Tahini brands vary in thickness. You might not need much water at all. Start with 1 tablespoon first, whisk in the olive oil, then add more water only if needed.
Make-ahead and storage: The dressing keeps well in the fridge for up to 1 week. Shake or whisk again before using.