Heat oven to 350ºF. Spray an 8-inch square glass baking dish with nonstick spray.
Bring 3 quarts water to a boil in an 8-quart pot over high heat and add several heavy pinches of salt. Prepare an ice bath in a bowl large enough to hold the broccoli. When the water boils, add the broccoli and cook for 1 minute. Drain the broccoli in a colander and immediately place in the ice bath to shock. Swirl around to cool completely, drain, and set aside.
Heat water in an 11-inch straight-sided saute pan over high heat for 30 to 45 seconds, then add the mushrooms. Cook, stirring occasionally, until the mushrooms collapse, 2 to 4 minutes, then add the butter. Cook, stirring occasionally, until browned, 7 to 10 minutes. Add the broccoli and ramen noodles and toss to combine.
Turn off the heat. Add the mayonnaise, yogurt, half of the cheese, the blue cheese dressing, eggs, 1/2 teaspoon salt, and the ramen noodle seasoning pack and toss to combine well. Transfer the mixture to the prepared baking dish and smash down with a spatula to compact the casserole. Sprinkle the top with the pepper and remaining cheese.
Cover with heavy-duty aluminum foil and bake on the middle rack of the oven for 45 minutes. Remove the foil and bake for an additional 15 minutes. Cool 30 minutes before serving.