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Trim endives and halve lengthwise. Cut pieces in half crosswise, then cut lengthwise into 1/4-inch-wide strips.
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Cut radicchio in half and discard core, then cut lengthwise into 1/4-inch-wide strips. Soak radicchio and endives in a large bowl of very cold water to crisp, 10 minutes, then drain and dry.
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Whisk together mustard, vinegar, sugar, salt, pepper, grapeseed oil, and sesame oil in another large bowl until emulsified.
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Add endives, radicchio, scallions, and sesame seeds and toss until coated well.