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Cut the cabbage into thin slices.
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Peel the apple, remove the pericarp and cut into small cubes.
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In a saucepan, pour and heat the olive oil.
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Add the red cabbage and brown for a few minutes.
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Add the diced apple and mix.
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Add broth and pour cold water until the top level of the cabbage.
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Add vinegar and sugar and bring to a boil.
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When boiling is reached, lower the heat and cover.
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Cook slowly and covered for at least 50 minutes.
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When the cabbage is melting, remove a ladle of juice in a bowl and dilute the cornflour in this juice.
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Pour the thickened juice in the saucepan.
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Mix and let the whole thicken for 5 to 10 minutes.
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Add salt and pepper.
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Serve the red cabbage on a mashed potato.