Shred and mince the chicken in your mini food processor and set aside.
Mince the broccoli and set aside.
In a pan, add your olive oil, the chicken, the broccoli, onion powder, garlic, and chilli powder.
Lightly sautee and remove from heat.
Start on the soup base by sauteeing onion and garlic in the butter.
Add the flour and mix well to make a rue.
Once browned, add in the both milks and the chicken broth and whisk continously on medium heat.
Once blended and warmed, add in the chicken and broccoli mixture and continue to mix.
Add in water to thin the mixture slightly.
Let come together to a light simmer, not boiling, and add the cheese.
Continue to mix on low to medium heat.
Once fully mixed in and no cheese or clumps are there, remove from heat. If you want you can further emulsify with a hand blender, however it's fine to leave as is (I enjoy it with bits of broccoili).
Pour in a bowl and serve with garlic toast or as is.