Preheat oven to 350°F. Coat a 9" x 9" baking dish with nonstick cooking spray then line with parchment paper. Set dish aside. In a mixing bowl, combine eggs and whipping cream. Mix well and set aside. Place mirliton slices in a large mixing bowl then season generously with salt, pepper, granulated garlic and nutmeg. Using your hands, rub mirliton and blend seasons well into slices. Place a layer of mirliton slices on the parchment paper in baking dish and sprinkle evenly with 2 tablespoons each of Parmesan cheese and Romano cheese along with pinch of tarragon and thyme. Continue layering until all mirliton slices are used up, remembering to sprinkle cheeses and herbs between each layer. Drizzle egg and cream mixture over mirliton and allow to soak through layers, pressing down firmly after each addition. Top with remaining cheeses. Cover with additional parchment paper then wrap loosely with aluminum foil. Bake 2 hours or until mirliton slices are tender, custard is set and internal temperature reaches 170°F. Uncover and bake until lightly browned, approximately 30 minutes. Remove from oven and allow to cool slightly. Place a layer of cling wrap then new aluminum foil over the top of the vegetables in baking dish. Cut a piece of thick cardboard to fit evenly into the 9" x 9" baking dish then place over the aluminum foil to serve as a press. Place 4 inverted coffee cups or cocktail glasses over cardboard and top with a weight such as a frying pan or 2 dinner plates stacked together. The weight over the cardboard will guarantee that the layers are firmly pressed together during the cooling process. Place in refrigerator and allow to cool a minimum of 12 hours. When ready to serve, remove weight, clinging wrap and foil then turn mirliton onto a cutting board. Remove parchment paper then cut into squares, triangles or circles as desired. Microwave or reheat in oven at 350° for 15 minutes before serving.