Wash the potatoes well, put them in a pan with cold water and cook for about 25 minutes from boiling: they must be fairly soft but still firm.
Drain, peel and coarsely cut them into pieces.
In the meantime, peel and wash the broccoli, divide them into florets, put them in a pan full of cold water and cook up to 5 minutes after boiling, then drain.
Brown the garlic, oil and chilli in a large non-stick pan, then remove the garlic and chilli and add the broccoli and potatoes.
Let it cook for a few minutes, then add a little broth and cook over low heat for 10-15 minutes (adding more broth if needed).
(Finally, if you wish, you can raise the heat for a couple of minutes to brown them slightly.)
The broccoli and potatoes are ready: season with salt and serve.
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