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1
Place the yeast, warm water, and honey in a small bowl, and stir to dissolve.
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2
When the yeast mixture is foamy, stir in the olive oil and salt.
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3
Place the flour and the yeast mixture in the bowl of an electric mixer.
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4
Using the dough hook, mix at low speed for about 8 minutes, then increase the speed to medium and knead until the dough is elastic and starting to pull away from the sides of the bowl, about 3 minutes.
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5
The dough should be smooth and firm.
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6
Ball up the dough, and place it in a large, well oiled glass bowl.
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7
Flip the dough ball to coat both sides with oil.
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8
Cover with plastic wrap, and let rise in a warm, draft free area for 2 hours, until doubled in bulk.
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9
Lightly flour a large cutting board or baking sheet.
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10
Divide the dough into four equal pieces, shape each into a ball, and allow the pieces to rest for 20 more minutes before cooking.
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11
When youre ready to cook the pizza, preheat the grill to high and the oven to 425F.
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12
Heat 1 tablespoon of the olive oil in a medium skillet over medium heat.
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13
Add the onion, bell pepper, and garlic, and saute until tender, about 5 minutes.
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14
Transfer to a glass bowl.
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15
Lightly flour a work surface, and roll out the four balls of dough into 6 inch circles that are 1/4 to 1/8 inch thick.
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16
Brush each round of dough with the remaining tablespoon of olive oil, and place on grill.
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17
Grill for 2 to 3 minutes on the first side.
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18
Flip, and cook for 1 more minute.
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19
Transfer the grilled crusts to a sheet tray, and repeat with the other dough balls.
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20
To assemble the pizzas, spread 1/4 cup of barbecue sauce evenly on each pizza, then top with 1/2 cup of chopped meat and a quarter of the sauteed vegetables.
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21
Sprinkle each pizza with a handful of mozzarella and a few pinches of grated Parmesan.
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22
Bake the pizzas for 10 minutes, or until the cheese is melted.
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23
Serve immediately.