Move rack to middle of oven and preheat to 325˚ F. Wash, peel, and thinly slice with mandoline all potatoes and yams. Place potatoes and yams, separately in large containers then fill with water to cover. Set aside.
Peel onions and cut into large dice. Set aside.
Wash and cut top and bottom off the fennel, chop fennel into large dice. Set aside.
Mince 2 cloves of garlic and 1 shallot. Set aside together.
Rinse thyme and remove from stem to get 1 cup. Set aside.
In large saute pan, heat butter on med-high heat until melted. Add garlic and shallots to pan, then add onions, fennel, and thyme. Stir mixture until everything is evenly coated with butter. Turn temperature down to med and stir occasionally. Keep stirring until fennel is soft and onions are translucent, remove from heat and let cool. Remove potatoes and yams from water and pat dry.
Spray large Pyrex dish with release spray, coating the whole dish evenly. Layer bottom of dish with yams, over lapping each row to fully cover bottom of the dish. Next, layer dish with potatoes, over lapping each row to fully cover the yam layer. Next, take 1/2 of onion mixture and evenly cover yam layer. Be careful not to move the yam layer. Then, evenly sprinkle 4 cups of blue cheese crumbles over onion layer. Repeat layers of yam, potato, and onion.
In medium sauce pan, add cream and salt. Heat cream on med heat until salt had dissolved.
In medium bowl, add eggs and pepper. VERY SLOWLY, add warm cream to eggs while constantly stirring eggs until all cream is incorporated. Slowly, pour egg mixture around the edges of the dish.
Place bread crumbs into medium mixing bowl, pour 3oz. of melted butter over crumbs. Toss crumbs to evenly coat with butter. Spread bread crumbs evenly over top of onions. Covering completely so the onions will not burn.
Bake at 325˚ for 60 min on middle rack. Let cool for 5 min. Cut into 3"x 3" squares and serve hot.
Reheating: Cover with foil and reheat at 350˚ F for 30 min.