In a large skillet, heat oil over medium. Add onions, and season with salt and pepper. Cover, and cook, stirring occasionally, until onions have softened, 8 to 10 minutes. Uncover; cook until onions are golden brown, 10 to 12 minutes more (if skillet begins to darken, add cup water).
Dividing evenly, spread cheese on 4 bread slices. Top with onions and figs; sandwich with remaining bread.