In a large bowl using a wooden spoon, or in a stand mixer fitted with the dough hook, combine the flour, sugar, yeast and salt. Add the water and mix until a soft ball of dough forms. Knead for 5 minutes on a floured work surface or in the stand mixer until smooth.
Form the dough into a ball and place in a clean, lightly oiled bowl. Cover with a damp dishcloth and let rest in a warm, humid spot for at least 1 hour (ideally 2 hours) or until the dough has doubled in volume.
Place the onions in a bowl and cover with cold water. Let soak for 1 hour. Rinse and drain.
Place a pizza stone directly on the barbecue grill. Preheat the grill, setting the burners to high.
In a bowl, combine the crème fraîche and mustard. Set aside.
Using a rolling pin or your hands, roll out the dough to a 12-inch (30 cm) circle. Place on a piece of parchment paper. Cover with the mustard mixture. Top with the onions and smoked meat.
Place the pizza (with the parchment paper) on the pizza stone. Close the lid and cook for 10 to 12 minutes or until the dough is golden. Maintain the barbecue temperature at 500°F (200°C) during cooking. Remove from the heat. Garnish with the gherkins and drizzle with mustard, to taste. Cut into wedges and serve.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.