Whisk eggs, milk, flour, and oil together until smooth. Stir in parsley and chives, then season with salt and nutmeg. Let rest for 30 minutes.
Peel the asparagus stalks and trim off the woody ends.
Melt butter in a pot over medium heat. Add diced onion and potato cubes, cook for 2–3 minutes, stirring, until softened. Pour in wine and scrape the bottom to deglaze. Add vegetable stock, bring to a simmer, cover, and simmer for 20 minutes. Remove from heat, stir in cress (reserve a few leaves for garnish), then blend until smooth. Stir in cream and season with salt, pepper, and sugar to taste. Keep warm.
Bring a pot of salted water to a boil over high heat. Add butter and sugar. Place asparagus stalks in the water and simmer for 12 minutes until tender.
While the asparagus simmers, heat clarified butter in a 16 cm (6.3 inch) non-stick pan over medium heat. Once hot, pour in batter to coat the bottom of the pan thinly. Cook for 1–2 minutes until golden brown on the bottom, then flip and cook the other side for about 30 seconds. Transfer to a plate. Repeat with remaining batter to make 4 crepes total.
Warm serving plates in a preheated oven set to 60°C (140°F). Drain the asparagus well. Place 3 asparagus stalks on each crepe, roll up, and place on a warm plate. Spoon sauce around the crepe, garnish with reserved cress leaves, and serve immediately.
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