Heat butter in a small saucepan and saute the shallot until it begins to soften (2-3 minutes).
Add the potato, cut into 1 inch pieces and the chicken stock. Pop the lid on and simmer until the potato is tender, about 15 minutes.
Remove the soup from the heat. Reserve two nice sprigs of chervil for the garnish, and add the rest of the chopped herb to the soup. Puree with a hand blender.
Return to the heat and add the double cream, heating through. Take care not to boil.
Add the lemon juice, season to taste and serve with a poached egg in the bowl, garnishing with the sprigs of chervil.