In a saucepan of salted boiling water, cook the potatoes and celery until the potatoes are tender. Drain and set aside.
In a large saucepan, bring the broth to a boil. Add the mussels. Cover and cook for 1 to 2 minutes or until mussels open. Drain and keep the cooking liquid for another use. Discard any closed mussels. Remove the mussels from their shells and place in a bowl. Refrigerate, if necessary.
Place about 54 half shells on a baking sheet covered with crumpled aluminum foil or coarse salt to stabilize the shells. Set aside.
In a small saucepan, soften the garlic in the butter. Add the flour and cook for about 1 minute, stirring constantly. Add the milk and pesto and bring to a boil, stirring with a whisk. Season with salt and pepper.
With the rack in the upper third of the oven, preheat the oven’s broiler.
Spoon the mussels and vegetables into the shells. Drizzle with the sauce. Bake for 2 to 3 minutes. Top with arugula and drizzle with oil. Serve immediately.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.