Heat 1 tbsp oil in a saucepan. Fry the garlic briefly, then add the onion and carrot. Saute till wilted.
Add the flour and saute in.
Now slowly add the milk and keep whisking till it thicken.
Add in the water and stock cubes and cook till the soup thickens.
In another pan, heat the rest of the oil and gently toss up the broccoli for a couple of minutes.
Add this into the simmering pot of soup along with the cheese and cook briefly just till the cheese is melted.
Add the remaining seasonings and switch off the flame.