Combine the yeast and 3/4 cup warm (110 degrees F) water in a large bowl; stir to dissolve the yeast, then set aside until foamy, about 5 minutes. Sift 3/4 cup flour into the bowl and blend with a wooden spoon until smooth.
Add 1 teaspoon salt, a few grinds of pepper and the honey and mix to blend. Sift the remaining 1 cup flour into the bowl and mix until incorporated. Transfer the dough to a floured surface and knead until smooth, 3 to 5 minutes. Brush a large bowl with olive oil and add the dough. Cover with plastic wrap and let rest in a warm place until doubled in volume, about 1 1/2 hours.
Roast the grapes.
Preheat the oven to 400 degrees F. Toss the grapes with 2 tablespoons olive oil on a parchment-lined baking sheet. Roast until wrinkled, 12 to 15 minutes. Meanwhile, bring the vinegar, sugar and mustard seeds to a simmer in a small saucepan over medium heat. Cook until the liquid is reduced by about half, 5 to 8 minutes. Remove the grapes from the oven (leave the oven on) and let cool slightly. Combine the grapes and the vinegar mixture in a bowl; set aside.
Cook the broccoli.
Heat a large ovenproof saute pan over high heat. When it gets hot, remove from the heat and add 3 tablespoons olive oil and the broccoli; season with salt and the red pepper flakes. Return to the heat and cook, stirring from time to time, until the broccoli chars, 10 to 12 minutes, adding 1 more tablespoon olive oil and the garlic during the last 2 minutes of cooking. (Add a splash of water if the pan is too dry.) Place the pan in the oven and cook until the broccoli is tender, about 5 more minutes. Set aside to cool; leave the oven on.
Prepare the ricotta.
Put the ricotta in a medium bowl. Season with salt and stir in the thyme and 2 tablespoons olive oil. Taste for seasoning. Set aside.
Roll out the dough.
Press the dough gently and turn it out onto a floured surface. Divide in half and roll each piece into a loose ball. Cover with a kitchen towel and let rest 15 minutes. Flatten the dough, then roll out each piece into an 8-inch round. Place on a lightly oiled baking sheet.
Cook the flatbread.
Heat the remaining 2 tablespoons olive oil in a 9-to-10-inch ovenproof saute pan over medium-high heat. When it begins to smoke lightly, turn off the heat and add one round of dough.
Return to medium-high heat and cook, pressing the dough gently with a spatula to keep it flat, until slightly brown on the underside, 2 to 3 minutes.
Season the dough lightly with salt and pepper, then flip and press with the spatula. Pour off any excess oil from the pan.
Add the toppings.
While the underside cooks, spread half of the ricotta mixture on top.
Arrange half of the grapes and broccoli on the ricotta. Transfer the pan to the oven to warm through, about 5 minutes.
Transfer the flatbread to a cutting board, cut it into slices and top with parmesan cheese. Repeat to make another flatbread.
You can make the dough and toppings in advance, then assemble the flatbreads at the last minute. "Cooking the broccoli a little past your comfort zone is good here - it will play nicely with the grapes."