Preheat oven to 375°F. Toss shallots with 2 tablespoons oil on baking sheet; spread in single layer.
Sprinkle with salt and pepper.
Bake until tender and golden brown, stirring occasionally, about 35 minutes.
Stir 2 tablespoons oil and breadcrumbs in skillet over medium heat until crumbs brown, about 4 minutes. (Shallots and crumbs can be made 8 hours ahead. Cover separately; keep at room temperature.)
Cook pasta in large pot of boiling salted water 10 minutes.
Add asparagus; cook until asparagus is crisp-tender and pasta is tender but still firm to bite, about 4 minutes.
Drain pasta and asparagus.
Transfer to large bowl. Immediately add blue cheese and shallots. Toss until cheese melts and pasta is well coated. Season with salt and pepper.