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1
Assemble the salad. Halve the radicchio lengthwise. Cut out the core, then roughly chop. Add to a bowl. Peel the orange-either with your hands or a knife. To do with a knife: cut the top and bottom off each orange. Stand on one end, then guide your knife from top to bottom, removing as little flesh as possible. Cut into thick rounds, then chop into chunks. Add to the radicchio. Stick in the fridge while you make the chicken.
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2
Halve the chicken breasts horizontally. Freezing them for about 15 minutes beforehand make this easier (a trick I learned from Cooks Illustrated). Place these between plastic film or parchment and pound to an even 1/4- to 1/2-inch thickness.
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3
Add the sesame seeds to a mortar. Use a pestle to roughly crush until some seeds are powdery, others whole. Stir in the salt. Dump this onto a plate and spread into an even layer.
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4
Add the peanut oil to a straight-sided cast-iron skillet-you want about 1/4-inch depth, so adjust as needed. Set on the stove over medium-high heat. Dredge the chicken pieces in the sesame mixture, pressing firmly to fully coat. Check if the oil is hot: If you drop in a few seeds, they should instantly sizzle, not drop to the bottom or burn. When it's hot, add the sesame-coated chicken. Depending on the size of your pan, you might have to do this in batches. If they're overcrowded, they'll steam versus brown.
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5
Cook for 3 to 4 minutes per side, until the outside is browned and the inside is cooked through. Transfer to a cooling rack to drain. Cook the remaining chicken if necessary, adding more oil to the pan if necessary.
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6
While those rest for a moment, dress the salad. Season with a pinch of salt and add the sesame oil. Toss. Taste and adjust the salt and oil to taste.
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7
Serve the sesame chicken immediately with the salad on top or alongside.
