Drop the Broccolini® into a saucepan of boiling salted water. Cook for 2 minutes or until bright green and stalks are just tender when tested with a skewer. Drain. Refresh in cold water. Pat dry with paper towel then roughly chop.
Place Broccolini® into a food processor with basil, chilli and garlic. Pulse until finely chopped. Add cashew nuts, pulse until well combined. Combine the olive oil and grapeseed oil in a jug. With the processor running, add the oil in a slow and steady stream until all the oil has been incorporated. Transfer pesto to a bowl.
Stir in pecorino cheese. Season with salt and pepper. Use immediately, or prepare for storing.