Arrange the rye bread slices on a baking sheet. Drizzle with olive oil, season with salt and pepper and bake in a preheated oven, 190°C (375°F), Gas Mark 5, for 5 minutes until crispy like croûtons. Remove from the oven and set aside.
Remove the leaves from the celery, reserving all the inside leaves. Finely slice 3 sticks and put them in a large salad bowl with the leaves, add the artichokes and parsley.
Thinly slice the smoked chicken breasts and add to the bowl with the celery and artichokes.
Make the dressing by whisking together the mustard, vinegar and oil. Drizzle over the salad and lightly mix.
Place a piece of rye toast on each serving plate and top with some salad.