Peel the shallots and halve them lengthwise. Heat 2 tablespoons of oil in a frying pan. Fry the shallots for 2-3 minutes over medium heat, turning them over. Meanwhile wash thyme, dab dry, pluck leaves from the stalks and chop finely.
Sprinkle shallots with 2 tablespoons of sugar and thyme. Continue frying until the sugar caramelises. Set aside. Wash the asparagus. Peel the white asparagus. Cut the woody ends off the asparagus.
Halve the asparagus and cut or slice lengthwise into very thin slices. Wash, clean and slice the strawberries. Season vinegar with salt, pepper and sugar, fold in 4 tablespoons of oil. Mix asparagus, strawberries and shallots with the vinaigrette and serve.