Combine unpeeled garlic cloves and lemon juice in a blender. Pulse until a coarse puree is formed, about 10 to 15 short pulses. Pour mixture into a fine mesh strainer set over a large bowl. Press out as much liquid as you can with the back of a spoon, then discard solids.

Stir cumin, cardamom and tahini paste into the bowl with lemon-garlic juice. The mixture will seize and turn pasty. Add cold water, a few tablespoons at a time, stirring in between each addition, until a smooth, thick but pourable sauce forms. Season to taste with salt and garnish with a good pinch of smoked paprika, if desired. Sauce will last in the refrigerator for up to 2 weeks.