Grilled Pizza with Goat Cheese, Tomatoes, and Thyme

In a small bowl, combine yeast and water. Cover and place in a warm part of the kitchen until mixture begins to bubble, about 10 minutes. In a food processor fitted with a knife blade, combine 3 cups flour, salt, 2 tablespoons olive oil, and yeast mixture. Process until a soft dough forms, about 45 seconds. If necessary, add more flour and pulse as needed until dough begins to pull away from the sides of the bowl. Turn dough onto a lightly floured work surface; knead about 2 minutes. Coat the inside of a large mixing bowl with oil. Coat dough thoroughly with oil. Place dough in bowl, cover with plastic wrap, and place in a warm part of the kitchen. Let rise until doubled in size, about 1 hour. Punch down dough. Cut in half and shape into 2 balls. Place on floured surface. Let rise again at room temperature for 30 minutes. Preheat gas grill to medium, or prepare a charcoal grill for direct grilling over medium heat. Roll dough balls into two 10-inch-round pizza crusts. Place pizzas on the grill and cook 3 to 5 minutes (the longer you cook them, the crispier they'll become). Using tongs, turn pizzas over and brush with remaining 2 tablespoons olive oil. Sprinkle each pizza with half the cheese, half the tomatoes, and half the thyme. Grill until the cheese has melted, about 5 minutes.