In a bowl, combine the water, oil, and honey. Set aside.
In a large bowl with a wooden spoon, or in a stand mixer (using the dough hook), combine the flour, yeast, and salt. Add the water mixture and stir until it forms a soft ball. Knead the dough for about 3 minutes on a floured surface or in the stand mixer.
Place the dough in a clean and lightly oiled bowl. Return the dough to coat with the oil. Cover the bowl with a damp cloth and leave in a warm and moist place for about 1 hour or until the dough has doubled in volume.
In a saucepan, sauté the chorizo and garlic in the oil for about 1 minute. Add the tomato paste, brown sugar, and wine vinegar and sauté for about 2 minutes. Add the tomatoes and bring to a boil. Simmer for about 10 minutes. Season with salt and pepper.
In a saucepan, soften the onion, mushrooms, and bell pepper in the oil. Season with salt and pepper. Pour the filling into the sauce. Stir thoroughly and let cool.
With the rack in the middle position, preheat the oven to 400°F (200°C). Line two large baking sheets with parchment paper.
On a floured work surface, cut the dough into 16 equal pieces. With a rolling pin, roll one piece of dough at a time into a 6-inch (15-cm) disk. Keep the remaining pieces under a damp cloth while making the pizzas.
Place about 3 tbsp of the filling in the centre of the disk of dough. Add 2 tbsp of cheese. Brush half of the edge of the dough with milk. Close the dough, sticking the dry side to the wetted side, forming a small turnover. Press the edges with your fingers. With a spatula, place the pizza on a baking sheet. Repeat with the remaining ingredients.
Brush the pizzas with milk and bake for about 20 minutes or until golden brown. Let cool for about 10 minutes. If they are frozen, reheat for about 15 minutes.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.