For the vinaigrette: Combine the wine, fennel seeds, peppercorns and thyme in a wide shallow saucepan. Bring to a boil and cook until reduced to 1/4 cup. Strain the mixture into a blender and discard the solids.
Add the vinegar and salt to taste and blend to combine. With the motor running, slowly add the olive oil until emulsified; add the honey to taste.
For the dough: Dissolve the yeast in the warm water in a large bowl and let stand for 5 minutes. Stir in 3 cups flour and the salt, stirring until smooth. Stir in an additional 2 cups flour. Continue adding the flour (up to 1/2 cup), 1 tablespoon at a time, stirring until the dough comes away from the bowl but is still sticky.
Turn the dough out onto a lightly floured work surface and knead with lightly floured hands. Start by slapping the dough onto the counter, pulling it toward you with one hand and pushing it away from you with the other. Fold the dough back over itself (use a bench scraper or a wide knife to help scrape the dough from the surface). Repeat until it's easier to handle, about 10 times. Finish kneading normally until the dough is smooth, elastic and soft, but a little tacky, about 10 minutes. Shape the dough into a ball and transfer to a lightly oiled bowl; turn to coat. Cover with plastic and let rise in a warm place until it doubles in volume, 3 hours. Press it with your finger to see if it's done; an indent should remain.
Prepare the charcoal in a chimney starter (allowing the charcoal to burn until all the charcoal is covered with a thin layer of gray ash). Add to the grill and create a two-level fire by spreading the coals out over half the grill bottom, piling them up in a mound 3 briquettes high, leaving the other half with no coals.
Remove the dough from the bowl, divide in half and shape each half into a ball. Brush with oil and set aside for 30 minutes.
Stretch and shape each ball of dough into a 12 by 10-inch rectangle or round on a flat surface. Brush the tops of each with oil and sprinkle with salt and pepper. Let rest for 15 minutes. Place on the grill directly over the coals, oiled side down, and grill until lightly golden brown, about 1 minute. Flip over and grill for 1 minute longer.
Place the flatbreads on a flat surface and divide the Monterey Jack cheese evenly over the top. Arrange the cut figs on top and the blue cheese around the figs. Return to the grill on the opposite side of the coals, for indirect heat, close the cover and cook until the cheese has melted and the figs are heated through, about 5 minutes. Remove from the grill and drizzle with some of the red wine vinaigrette and garnish with parsley leaves. Cut and serve immediately.