Position racks in the upper and lower thirds of the oven and preheat to 450ºF (230ºC).
Make the pizza dough and while it rises, prepare the other ingredients.
Use a T-shaped vegetable peeler to peel the pumpkin and cut it in half with a large, sharp chef's knife. Scoop out and discard the seeds and strings. Slice the pumpkin flesh into 1/2-inch (1 cm) thick strips. Place the squash in an even layer on a rimmed baking sheet rubbed with olive oil. Drizzle the squash with 2 tablespoons more olive oil, sprinkle with a few pinches of salt and pepper, and toss to coat. Place on the upper rack of the oven and roast until tender and just beginning to turn golden, 15-20 minutes. Remove from the oven.
When the dough has risen, line a rimmed baking sheet with parchment paper and drizzle with 1 tablespoon olive oil. Scrape the dough onto the pan, drizzle with another tablespoon of oil, and use your fingers to gently spread the dough into a thin, even layer that completely fills the pan, smoothing the edges as best you can. Drizzle with a bit more oil, cover the pan with a second baking sheet or large cutting board, and let rise in a warm place until the dough feels quite spongey to the touch, about 15-20 minutes. Uncover the pan and place in the oven on the lower rack. Bake until the edges are golden and the top of the dough is dry and firm, 10-15 minutes.
Remove the crust from the oven and top with the gruyere, squash, and onion. Return to the oven, on the upper rack this time, and bake until the cheese is bubbling and the dough is golden, 10-15 minutes.
Meanwhile, place 3 tablespoons of olive oil in a smallish (8-inch) skillet and heat over a medium-high flame until it shimmers. Add the sage leaves in an even layer - they should sizzle and hiss - and cook, tossing gently with tongs, until the sage turns dark green, 2-3 minutes. Remove the sage to a small plate; it should crisp up as it cools. Put the garlic through a press and into a small, heat-proof bowl, and pour in the hot sage oil. Let sit until needed.
When the flatbread has baked, scatter with the sage leaves, and drizzle with the garlicky sage oil leaving behind the garlic for another use (unless you are a garlic fiend, in which case, by all means, add it as well). Top the flatbread with a sprinkle of flaky salt and coarsely ground black pepper. Carefully remove from the pan and place on a large cutting board, cut into pieces, and serve immediately.
Should you have leftover flatbread, store it airtight in the refrigerator and reheat pieces in a cast iron skillet set over a low flame. This will crisp the crust by the time the cheese is heated through.