Preheat oven to 350°. Butter two 9- by 13-in. baking dishes. Set aside. In a small saucepan over low heat, melt 1/3 cup butter. Set aside and cool slightly.
In a large bowl, combine flour, cornmeal, sugar, baking powder, and 1/2 tsp. salt. Stir in 1 1/4 cups milk, 2 eggs, and melted butter. Pour batter into a buttered baking dish and bake until a toothpick inserted in the center comes out clean, 30 to 35 minutes. Let cool and then cut cornbread into bite-size pieces.
Meanwhile, in a small bowl, soak porcini in 1 3/4 cups hot water for 15 minutes. With a slotted spoon, transfer porcini to a cutting board and roughly chop. Reserve porcini and soaking liquid.
Melt remaining 1/4 cup butter in a large frying pan over medium-high heat. Add leeks, garlic, shallots, porcini, sage, and remaining 1 tsp. salt. Cook, stirring, until leeks and shallots are soft, about 5 minutes. Carefully pour in porcini liquid, leaving behind any grit at the bottom of the bowl.
In a very large bowl, whisk together remaining 4 cups milk and 6 eggs. Stir in leek mixture. Add baguette cubes and stir. Add cornbread cubes and fold gently to mix. Transfer to second buttered baking dish and break gorgonzola into small pieces while scattering over the top. Bake until set, about 40 minutes. Let sit 5 to 10 minutes before serving.
Note: Nutritional analysis is per serving.