Wash the rocket and dry it thoroughly with a salad spinner or kitchen paper. Cut or break off the lower tough parts of the green asparagus. Wash the asparagus and pat it dry.
Heat a dry frying pan over medium-high heat and toast the pumpkin seeds for a few minutes until golden brown. Remove them from the pan immediately and let cool. In a bowl, toss the asparagus with half of the olive oil, some salt and freshly ground black pepper. Heat a griddle pan and cook the asparagus for five to seven minutes until just tender on all sides. Remove from the pan and let cool slightly.
Whisk together a dressing from the remaining olive oil, balsamic vinegar, salt and black pepper. Place the rocket, smoked chicken strips and grilled asparagus in a large bowl. Pour the dressing over the ingredients and gently toss everything together.
Divide the salad among the plates or serve in a large bowl. Sprinkle the toasted pumpkin seeds over the dish and serve immediately.