Cover the chickpeas with 3 cups water in a large pot with 1 teaspoon baking soda and refrigerate 8 hours or overnight to soak.
The next day, strain the chickpeas and discard the soaking liquid. Rinse the chickpeas and return them to the pot. Add the remaining teaspoon baking soda and water to cover by about 3 inches. Bring to a boil over high heat, then turn the heat down to a simmer and cook, skimming off and discarding any foam that rises to the surface, until the chickpeas are very soft and creamy (not crumbly) when pressed between a thumb and forefinger, about 40 minutes. If the liquid boils off while cooking, add more water to cover and continue to cook.
Strain the chickpeas and discard the liquid. Let the chickpeas sit in the strainer to drain and dry out for 5 minutes. Put the chickpeas in the bowl of a food processor along with the tahini, lemon juice, garlic, all but a pinch of the dill and 1 1/2 teaspoons salt and process until the mixture is a paste, scraping down the bowl as necessary. With the motor running, slowly pour in 1/4 cup of the ice water and continue to process until the mixture is smooth and light, about 5 minutes, adding more water a tablespoon at a time until the desired consistency is reached.
Transfer the hummus to a shallow bowl and cover by lightly pressing plastic wrap directly onto the surface of the hummus; let sit at room temperature until ready to serve, up to 1 hour. (The hummus can also be made a day ahead and refrigerated. Take the hummus out of the refrigerator to warm up 30 minutes before serving.)
Before serving, remove the plastic wrap from the hummus. Smooth the outer rim of the hummus with the back of a large kitchen spoon, creating a slight well in the center. Dollop the yogurt in the center. Scatter the radish slices and capers on top, sprinkle with the reserved dill and serve with slices of pumpernickel bread and cucumbers.
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