1. Preheat oven to 425 degrees. Toss bread-crumbs with oil; season with salt and pepper. Place on a rimmed baking sheet and toast until crisp and just beginning to brown, about 5 minutes.

2. Increase oven temperature to 475 degrees. Bring a large pot of salted water to a boil; add asparagus. Return to a boil and cook until crisp-tender, 30 to 60 seconds. Transfer to a plate. Add potatoes to pot; cook until just tender, 8 to 10 minutes. Drain. Arrange potatoes in the bottom of an 8 1/2-by-11 1/2-inch or 2-quart baking dish (about 1 1/2 inches deep).

3. Melt butter in a saucepan over medium heat. Add flour; cook until it has a slightly nutty aroma, about 30 seconds. Gradually (to avoid lumps) whisk in milk. Bring mixture to a boil and cook, whisking, until thickened slightly, about 1 minute. Remove from heat; add both cheeses and whisk until melted. Season with salt and pepper.

4. Pour half of sauce over potatoes. Arrange prosciutto and half of asparagus on top. Drizzle with remaining sauce. Top with remaining asparagus, then bread-crumbs. (Dish can be made to this point and refrigerated in an airtight container up to 1 day; add 10 minutes to baking time.) Bake until bubbling around edges, 10 to 12 minutes. Let cool slightly; serve, sprinkled with more Pecorino and chive blossoms.