Preheat your oven to 425°F (220°C). Toss the breadcrumbs with olive oil and season lightly with salt and pepper. Spread them on a baking sheet and bake until lightly golden and crisp.
Remove the breadcrumbs from the oven and set them aside. These toasted crumbs will add a delicious crunchy topping later. Increase the oven temperature to 475°F (245°C) for baking the gratin.
Bring a large pot of salted water to a boil. Add the asparagus pieces and cook briefly until crisp-tender. This quick blanching preserves the bright green color and fresh flavor.
Transfer the asparagus to a plate or bowl. Let it cool slightly while you prepare the potatoes. Avoid overcooking to maintain a pleasant texture.
Using the same pot of water, add the sliced potatoes. Cook them until just tender but not falling apart. They should still hold their shape when handled.
Drain the potatoes carefully. Arrange them evenly in the bottom of a greased baking dish to create the first layer of the gratin.
In a saucepan over medium heat, melt the butter. Add the flour and whisk continuously for about 30 seconds until it develops a slightly nutty aroma.
Gradually whisk in the milk to prevent lumps. Continue whisking until the mixture thickens slightly. Remove from heat and stir in the goat cheese and Pecorino Romano until smooth.
Pour half of the cheese sauce over the potato layer. Arrange the optional prosciutto slices and half of the asparagus over the sauce.
Add the remaining sauce evenly across the dish. Finish with the rest of the asparagus, making sure the vegetables are distributed evenly throughout.
Place the baking dish in the hot oven and bake until the sauce bubbles around the edges. This usually takes about 10 to 12 minutes.
Remove the dish and sprinkle the toasted breadcrumbs over the top. Let the gratin cool for a few minutes before serving.
Just before serving, sprinkle with extra Pecorino Romano cheese and chopped fresh herbs if desired. The herbs add freshness and color to the finished dish.
Serve warm while the sauce is creamy and the topping remains crisp. Every bite should include potatoes, asparagus, and cheesy goodness.