1. Prepare the oven to heat to 425F, and line a baking pan with foil. Then, break the woody base off the asparagus stems and toss them away. Rinse the trimmed stalks in a colander under running water. Then, blot them dry with paper towels, and arrange them in one layer in the lined baking pan.
2. Bake the stems in the oven for 10 to 12 minutes (thin stalks will take about 7 to 10 minutes). The branches are done when the thick part is easy to pierce with a fork.  Move the roasted asparagus to a serving bowl and sprinkle the Parmesan cheese and red pepper flakes. Then, serve hot or allow it to cool beforehand.

More ways to check for the cooking time in roasted asparagus can be found in this video.