In a large bowl or the bowl of an stand mixer, mix the water, yeast, salt, sugar and olive oil. Let it stand for about 2-3 minutes. Add the flour and mix, either with a wooden spoon and some good elbow grease or the paddle attachment of the stand mixer – mix the dough until it is just combined, without kneading.
Lightly cover the bowl and place in a warm spot to let the dough rise until the dough has doubled in size and is flat on top, about 2-3 hours. Refrigerate the dough, lightly covered, for at least 30 minutes or until you are ready to use (this can be done several days in advance, if you wish, up to 12 days).
Make the flatbreads:
Dust the dough lightly with flour, then divide the dough into three pieces, sprinkling with a little more flour and forming them into balls by stretching the dough underneath. Flatten the dough using your hands until they are about 1/2 inch (for a thicker crusor thinner (for thin crusand about 10 inches in diameter, depending on the size of your skillet. Let rest while you heat your skillets and gather your toppings.
Heat a skillet(s) over high heat. Take the dough and lightly spray with water or brush with melted butter. Place wet side down on the hot skillet and cover. Cook for about 2-3 minutes, and when brown, slightly spray/brush the top with water or butter and flip the dough. Quickly spread the pesto onto the dough, leaving about a 1 inch margin from the edges. Sprinkle with goat cheese, butternut squash, artichokes, and season with salt and pepper. Scatter some arugula on top and cover, letting it cook for about 2 minutes more. Carefully transfer the flatbread onto a cutting board and repeat with remaining dough.
Serve the flatbreads with more arugula and a drizzle of olive oil and balsamic vinegar.
Make it ahead: After rising, the dough can be refrigerated for up to 12 days. See recipe for complete details.Flatbread dough from Olive Oil Dough, The New Artisan Bread in Five Minutes a Day by Jeff Hertzberg, M.D. and Zoe Francois (Thomas Dunn Books, 2013).