Trim breasts of any skin or fat. Sprinkle with a liberal amount of salt and freshly ground pepper. Pat this well into the flesh. Dredge lightly in flour.
In a heavy skillet heat olive oil. Add to this the lump of butter. When the oil and butter are very hot put the chicken breasts in and saute them until they are golden brown and just a tiny bit less than perfectly done. Remove them from the pan and place on a clean towel on a platter. Put aside where it is warm.
If the pan is too hot, allow it to cool a bit before adding the chopped shallots. Saute until translucent. Now add fresh lemon juice and stir until just slightly reduced. Add sherry (Tio Pepe or something similarly dry and of a comparable thinness), stirring and cooking until liquid has been reduced by hal£.
When there is a nice melange remaining in the pan, add the heavy cream. Again, stir and reduce for about 10 minutes over a moderate flame. Taste as you go and amend with salt and fresh pepper if you so desire. When the sauce is as you like it, return the chicken breasts to the pan and let them stay in the sauce, covered, over a very low heat until ready to serve.
Remove chicken and sauce to a heated platter or serving dish. Garnish with thin slices of lemon and fresh greens.