Bring a large pot of lightly salted water to a boil. Cook shell pasta in the boiling water, stirring occasionally until still firm to the bite, about 9 minutes. Drain.
Preheat oven to 350 degrees F (175 degrees C). Butter a 9x13-inch baking dish.
Heat olive oil in a large pot over medium heat. Add mushrooms, onion, and salt and pepper to taste. Cook and stir until mushrooms have browned and onion is translucent, about 7 minutes. Add radicchio, garlic, and sage; cook until radicchio has wilted and garlic is fragrant, about 3 minutes. Remove from heat and stir in pasta.
Melt butter in a saucepan over medium-high heat. Whisk in flour; cook until foaming. Pour in milk, whisking constantly, until mixture comes to a boil and thickens, about 5 minutes. Remove from heat; whisk in Asiago cheese, heavy cream, 1 cup Parmigiano-Reggiano cheese, 1/2 teaspoon salt, and 1/4 teaspoon black pepper until sauce is melted and smooth.
Pour sauce over pasta mixture; stir until thoroughly combined. Transfer to prepared baking dish. Top with remaining 1/2 cup Parmigiano-Reggiano cheese and panko.
Bake in the preheated oven until bubbly, about 30 minutes. Broil until topping is golden brown, about 1 minute.