Method
- Soften the onion in the oil in a large pot over medium heat 5 minutes, until soft and clear, add the garlic for a minute, then stir in the flour and cook 1 minute more.
- Whisk in the broth and milk a little at a time. Add the potatoes and the chicken breast halved lengthwise and simmer gently 12 minutes, until the chicken reads 165°F (74°C), stirring often so the bottom does not catch. Lift it out.
- Add the broccoli and simmer 6 minutes more, until the potatoes are soft through. Take the pot off the heat, let it stand 5 minutes, then blend a third of it with a stick blender.
- Stir in the cheddar a handful at a time until it melts, shred the chicken back in and finish with the smoked paprika.
Tip. Add the cheese off the heat, a handful at a time. Boiled, cheddar splits into oil and grit; stirred into a soup that has stopped bubbling, it melts smooth.
Keep. Keeps 4 days chilled, freezes 2 months. Reheat gently and never let it boil.
Pack it. Travels in a flask; it thickens as it stands, so loosen it with a splash of water.