Heat a little bit of olive oil in a pan over medium-high. Add broccoli and mushrooms, and stir-fry until cooked (around 5 minutes). Remove from heat and set aside. 

Combine milk, water, and quinoa in a large saucepan. Bring to a boil, then reduce heat to low. Simmer, stirring regularly, until most of the liquid has been absorbed.

Add vegetables, cheese and salt & pepper to the pot of quinoa and stir to combine. Cover and set aside. 

Fry a sunny side–up egg. 

Transfer the quinoa to a bowl, then top with the egg.