Clean Potatoes; Boil Until Just Tender; Cool. Peel Them And Place On Platter. Cut 6 Very Thin Slices From The Cheese And Grate The Rest. Wash Tomatoes And Cut Off Tops; Scoop Out Pulp And Pass Thru A Strainer; Reserve. Salt And Pepper The Tomato Cases And Turn Upside Down To Drain. Sprinkle The Potatoes With The Parsley And Put Them Into The Tomatoes, Then Place The Stuffed Tomatoes In A Shallow Pan. Drizzle Some To The Oil Over The Top, And Sprinkle With Part Of The Grated Cheese. Pour The Remaining Oil And Tomato Pruee Into The Pan. Bake In A Preheated 350 F. Oven For 15 Min. Remove From Oven. Spoon Up Some Of The Oil From The Pan And Baste The Tomatoes With It, Then Put A Slice Of Cheese On Each Tomato, And Break An Egg--Be Careful Not To Break The Yolk--On Top. Sprinkle The Eggs With Salt, Pepper, The Rest Of The Cheese, And The Bread Crumbs. Return To The Oven To Bake For Another 15 Min. At 300 F. Serve Immediately.