To make the flatbread dough, mix together the olive oil, warm water, yeast, and sugar. Allow to sit for five minutes to rise. Blend the salt with the flour and mix with the wet ingredients to form a somewhat moist dough.
Knead the dough for about five minutes adding just a bit of flour if it becomes too sticky. Knead until a smooth dough forms. Divide into two balls and set aside covered in a warm place to rise until doubled, usually about 1 hour.
Preheat the oven to 450 F.
In a large sauté pan heat the olive oil over medium heat. Add the mushrooms and sprinkle with a bit of sea salt to taste. Sauté until they just begin to turn a light golden-brown colour. Add the sliced shallot and cook for an additional 2-3 minutes until the shallot is sweet, soft, and also gently caramelized. Adjust seasoning as desired with salt and pepper, and set aside to cool while the dough rises.
To assemble, roll each flat dough ball into a very thin circle, approximately 8" in diameter. Place the rolled dough onto a sheet pan or pizza pan that is greased with olive oil, lined with parchment, or dusted with cornmeal.
Arrange the caramelized mushroom-shallot mixture evenly over both pieces of dough. Sprinkle each with equal portions of crumbled blue cheese, another drizzle of olive oil, and additional fresh ground pepper (if desired). Slide the flatbread in to the preheated oven and bake for approximately 15 minutes until the cheese is melted and beginning to caramelize and the crust is golden brown and slightly puffed. Rotate the flat bread halfway through the cooking process to ensure that each side cooks evenly.