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1
Remove hard ends of asparagus. Preferably this is done by grabbing each end of your asparagus and bending it until it breaks. It should naturally break where it's tough.
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2
Boil asparagus ends (normally they'd be tossed) and potatoes in vegetable stock and water as necessary to cover everything until potatoes are nearly done, about 20 minutes.
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3
Meanwhile, remove tips of half of your asparagus. Toss all asparagus (and tips) in olive oil and all seasonings, and broil on high for 20 minutes, tossing regularly to prevent burning. Remove when some browning all over. If you think you've overdone it, just taste one before throwing. The asparagus carmelizes fast and may look burned when it's still fine. Firmness will vary with thickness of asparagus.
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4
Remove potatoes and asparagus ends from liquid. Toss asparagus ends. Add roasted asparagus, but reserve tips. Peel potatoes and chunk before adding back to pot. Chunk up potatoes to make blending easier.
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5
Continue to boil at high for 5 minutes or until potatoes are fully cooked.
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6
Blend in batches or with wand blender.
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7
Return to heat, add half of asparagus tips and let cook for another 10 minutes. Taste and adjust seasoning. Add water if too thick.
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8
Remove from heat, and add cheese. If using a microplane to grate your hard cheese, use about 1 cup of loosely packed cheese.
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9
Serve with a few asparagus tips added to top of each serving.
