Pulse flour and eggs in a processor until a dough forms.
Wrap dough in cling film and rest in the fridge for 30 minutes.
Pass floured dough through a pasta machine, decreasing thickness settings gradually.
Cut the pasta into shapes and dust with semolina.
Boil pasta in salted water until al dente, drain, and reserve some water.
Griddle oiled asparagus until marked, then add butter, pasta water, and lemon juice.
Fry breadcrumbs, lemon zest, garlic, and thyme in oil until golden.
Stir chopped parsley into the breadcrumb mixture.
Cut griddled asparagus into pieces and toss with pasta and some breadcrumbs.
Serve in warm bowls topped with the remaining breadcrumb mixture.