In a small saucepan over low heat, melt the 6 T. butter. Add in the flour and stir until blended; do not brown. Remove from heat and set aside. This is done first so the roux has a moment to stabilize while you focus on the vegetables.

In a large saucepan, melt the 2 T. butter. Add onion; cook until translucent and soft to release their natural sugars, which provides a sweet base for the savory broth.

Add chopped broccoli florets, cook and stir about 6 minutes. This initial sauté is crucial because it softens the broccoli slightly and allows the butter to coat the florets before we add the liquid.

Add the chicken broth. Increase the heat at this point and bring to a boil.

Whisking constantly, add the flour mixture (roux). This is the moment where your roux science pays off; the whisking ensures the roux particles disperse before they begin to thicken. Cook and stir until soup is thickened and bubbly. You will see the liquid transform from a thin broth to a glossy, unified soup.

Lastly, add in the salt, pepper, and half & half. Heat through and serve hot. Note: The soup will thicken upon standing because the starch molecules continue to absorb moisture as the soup begins to cool slightly.

For a hybrid texture (recommended): Use an immersion blender for about thirty seconds to break down roughly half of the broccoli while leaving visible florets.