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Trim - cut off the top - and clean the radicchio. Dry it with a kitchen cloth and set it aside.
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If needed, unshell the walnuts. Transfer them to a food processor, add the olive oil, and pulse until coarsely chopped.
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Cut the parmesan into small pieces and add it to the food processor as well. Add a pinch of salt and a few grinds of pepper (4-6). Pulse for a few seconds to amalgamate.
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Add the radicchio and pulse until your desired consistency: crunchy or creamy. The important thing is that the ingredients are well combined. Help yourself with a spatula to press down what sticks to the walls.
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Ready! Cook any short or long pasta according to the package directions, and simply season each serving with one to two tablespoons of your Italian radicchio pesto.