Heat oil in a large pot over medium-high heat. Add onions, and cook, stirring occasionally, until translucent but not brown, about 15 minutes.
Stir in salt, stock, and water. Bring to a simmer, and cook for 15 minutes.
Remove from heat, and let cool for 20 minutes. Working in batches, puree in a blender, starting on low speed and gradually increasing to high, blending until soup is smooth.
Divide soup among 4 bowls, drizzle with oil, and serve with flatbread on the side.