1. To make the dough, combine the yeast, water, and 1 tablespoon of the flour in a medium bowl, and whisk to blend. Let the mixture stand until it is slightly foamy, about 5 minutes.
2. Combine the remaining flour and the salt in a large bowl, and stir to blend. Add the yeast mixture, the 2
tablespoons oil, and the cream. Stir well with a heavy wooden spoon until the dough begins to come together and pull away from the sides of the bowl. Turn it out onto a lightly floured surface and knead for 4 to 5 minutes into a smooth, but slightly sticky, dough. Oil a clean bowl with 1 teaspoon of the remaining vegetable oil and place the dough in the bowl, turning to coat it. Cover the bowl with plastic wrap or a clean kitchen towel, and allow the dough to rise in a warm, draft-free place until doubled in size, about 40 minutes.
3. Lightly grease a baking sheet with the remaining 1/2 teaspoon vegetable oil. Divide the dough in half, and form each piece into a ball. Place them on the prepared baking sheet, cover with plastic wrap, and refrigerate until doubled in volume, about 2 hours.
4. Preheat a grill to medium. Clean the grill very well with a brush, and lightly grease the grate with vegetable oil.
5. Combine the goat cheese and 3 tablespoons of the honey in a bowl, and mash with a fork until smooth.
6. Remove the dough from the refrigerator and roll each ball with a rolling pin on a floured surface into a 10-inch
round. Transfer one of the rounds to a pizza peel sprinkled with cornmeal. With a quick flick of the wrist, slide the pizza dough onto the grill and cook on one side, rotating it with a spatula to mark it evenly, until golden brown, 3 to 4 minutes. Remove the dough from the grill and place it, grilled side up, on a large cutting board. Repeat with the remaining dough.
7. Spread half of the goat cheese mixture across each crust, using a rubber spatula. Arrange half of the sliced figs across the top of each crust.
8. Transfer the pizzas to the grill, cover, and cook until golden brown, rotating them with a spatula to keep them from burning, 3 to 4 minutes. Transfer the pizzas to serving plates, and sprinkle them with the black pepper and the mint leaves. In a small bowl, combine the remaining 2 tablespoons honey with the Armagnac. Drizzle each pizza with half of the honey-Armagnac mixture, and serve immediately.
Yield: Two 10-inch pizzas, 6 to 8 servings