Step 1

Preheat oven to 425 degrees. Toss breadcrumbs 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.

Step 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).

Step 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.

Step 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.