Clean and slice the celery and carrots. Clean the leek and cut into pieces approx. 2 cm long. Clean the peppers and cut into lozenges. Rinse the mushrooms and pat dry.
Heat vegetable oil in a wok or high pan. Peel off the garlic clove, mash it and fry it with the vegetables for about 5 minutes, stirring constantly. Season with salt and pepper.
Mix the honey, soy sauce, sherry, sherry vinegar and sesame together. Add to the vegetables and cook covered for about 10 minutes over a low heat. Season the Asian vegetables to taste and serve immediately.