Wash the potatoes, chop into 3cm chunks and cook in a large pan of boiling salted water for 12 minutes, or until tender. Meanwhile, line up the asparagus, trim off the woody ends, then slice the stalks 1cm thick, leaving the tips whole.
Drain the potatoes and steam dry for 2 minutes, then return to the pan and mash well. Taste and season to perfection with sea salt and black pepper, then tip on to a clean work surface. Fill the empty pan with boiling kettle water and place on a high heat. Use your hands to scrunch the flour with the potato, then divide into 24 pieces. Squeeze each in your palm to compress, into little uneven gnocchi, then drop into the boiling water for 1 minute, or until they float.
Meanwhile, put the asparagus into a large non-stick frying pan on a medium-low heat with 1 tablespoon of olive oil, stirring occasionally. Strip in most of the thyme leaves, then use a slotted spoon to add the gnocchi straight in. Finely grate over most of the Parmesan and toss well, adding 100ml of gnocchi cooking water to emulsify it into a nice sauce. Taste, season to perfection, then dish up. Grate over the remaining Parmesan, strip over the remaining thyme, and finish with a little drizzle of extra virgin olive oil.