Bring a large pot of well-salted water to a boil.
In a 12-inch skillet, heat 3 Tbs. of the oil over medium heat. Add the breadcrumbs and cook, stirring occasionally, until they’re crispy and golden brown, about 5 minutes. Transfer to a medium bowl and stir in the Parmigiano and a pinch of salt. Wipe the skillet clean with a paper towel.
Cook the pasta in the boiling water until al dente. Reserve a few tablespoons of the cooking water and drain the pasta.
Heat 1 Tbs. of the oil over medium-high heat in the skillet. Add the asparagus and cook, stirring frequently, until crisp-tender, about 4 minutes. Lower the heat to medium low and push the asparagus to the side. Add the remaining 1 Tbs. oil and the garlic and cook, gently mashing with the tip of a wooden spoon or spatula until fragrant, about 30 seconds. Toss the garlic with the asparagus. Remove from the heat.
Stir in the olives and lemon zest, and season with salt and pepper to taste. Add the pasta to the skillet, stirring to blend. Add enough reserved cooking water to slightly moisten, as needed, and drizzle with olive oil to enrich. Serve garnished with the breadcrumbs.