Preheat the oven to 200°C.
Simmer soup ingredients except oil in a saucepan for ten minutes until broccoli is soft.
Blend the soup with a hand blender until smooth.
Pulse butter and flour in a food processor to form fine breadcrumbs.
Add the egg, salt, and pepper to the processor and blend.
Gradually add milk while blending until a soft dough forms.
Shape dough into rounds with floured hands and place on a baking sheet.
Top with cheddar and bake for ten minutes until golden.
Serve soup drizzled with oil alongside a warm scone.