Add the butter to the onion and garlic, whisking it in till it melts fully.
Sprinkle the flour into the pan, while continuing to whisk to allow the flour to combine with the melted butter without formation of any lumps. It should form a thick, buttery paste.
Once the flour has incorporated into the melted butter and the smooth paste has formed slowly add the milk while whisking to create the sauce.
Finish off the sauce by whisking in the cream.
Allow the sauce to simmer for a few minutes on low heat while whisking.
Once the sauce has simmered and the flour has cooked, add the grated cheese and whisk it into the sauce so it combines well.
When the cheese has melted, return the browned chicken fillets and the cut broccoli florets into the pan. Allow the chicken and broccoli to simmer and cook at a low temperature for 10 minutes.
Add some crumbed feta to dish just before you remove it from the heat.