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Preheat the oven to 425°F. In a heatproof bowl, cover the bulgur with the boiling water. Cover the bowl with a plate and let stand until the water has been absorbed and the bulgur is tender, about 30 minutes.
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Meanwhile, on a rimmed baking sheet, coat the chicken breasts with 1 tablespoon of the grapeseed oil and season with salt and pepper. Roast the chicken until the internal temperature registers 165°F with an instant-read thermometer, 15 to 18 minutes; let cool. Slice the breasts on the diagonal about 1/4-inch thick.
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In a small bowl, whisk the orange juice with the basil, lemon juice, scallions, and the remaining 1/4 cup of grapeseed oil; season the vinaigrette with salt and pepper.
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In a large bowl, toss the bulgur, chicken, avocados, fennel, and tomatoes with the vinaigrette; season with salt and pepper. Mound the salad onto plates and serve.