To make the flat bread dough, mix together the olive oil, warm water, yeast, and sugar. Allow to sit for five minutes to bloom. 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, until a smooth dough forms. Divide in to two balls and set aside covered in a warm place to rise until doubled, for about 1 hour.
Meanwhile make the mushroom topping. In a large saute pan heat the olive oil over medium heat. Add the mushrooms and sprinkle with a bit of sea salt to taste. Saute until they just begin to turn a light golden-brown color. 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. Alternatively, you can use your bread machine or stand mixer to mix and knead the dough.
Preheat the oven to 450 F.
To assemble, roll each flat dough ball in to a very thin circle, approximately 8" in diameter. Place the rolled dough on to a sheet pan or pizza pan either 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, and another drizzle of Mushroom-Sage Olive Oil, and additional fresh ground pepper (if desired). Slide the flat bread 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 half way through the cooking process to ensure that each cooks evenly.