To make the dressing, combine the pomegranate molasses, oil and lemon juice in a small bowl. Season and set aside.
Combine the radicchio and oakleaf lettuce in a large bowl and shred the chicken over the salad leaves, discarding the skin. Scatter over the fig and cucumber, then, using a vegetable peeler, shave over the Manchego.
Drizzle the dressing over salad and serve with slices of sourdough.