Peel the asparagus and cut off the ends. Simmer in salt water about 15 minutes. Remove, drain well and pat dry. Season with salt and pepper. Roll in flour. Beat the egg with oil. Dip the asparagus tips in the egg and roll in breadcrumbs. Cook in hot butter about 4 minutes until golden brown. Drain on paper towels.
For the dip: Rinse the herbs and chop finely. Mix with cream briefly. Peel and press the garlic into the dip. Season with salt and pepper. Scrub and peel the potatoes. Cut in half and cook in salt water for about 20 minutes. Drain. Heat the potatoes in a pan of butter.