In a medium stockpot, melt butter over medium heat. Stir in onions, and saute until transparent, about 4 minutes. Add radish greens, and cook until wilted, about 4 minutes. Add potatoes and chicken stock, and cook, stirring occasionally, until potatoes are tender, about 35 minutes.
Working in batches, pass the mixture through a food mill into a medium bowl. Stir in cream, and season with salt and pepper. Strain the pureed mixture through a fine-mesh sieve into the original pot. Bring soup just to a simmer over medium heat. Serve garnished with radish zest and chervil.