Heat the olive oil in a saucepan over medium heat.
Add the garlic and ginger and cook until the garlic is just browned.
Remove from the heat and reserve.
In a large non-reactive bowl, whisk together the lemon juice, walnut oil and salt and pepper, then add the garlic and ginger.
Using a vegetable peeler, peel the asparagus lengthwise into ribbons. Add to the bowl with the dressing. Let rest to infuse for 1 hour.