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Process red peppers, almond butter, vinegar, 4 tablespoons oil, and ½ teaspoon salt in a blender, scraping down sides as needed, until smooth, about 1 minute.
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Preheat grill to medium-high (400°F to 450°F). Cut cauliflower lengthwise into 4 “steaks” (¾ inch thick), leaving stem intact. Brush cauliflower with 2 tablespoons oil; season with black pepper and remaining 1 teaspoon salt. Grill cauliflower, covered, turning occasionally, until stem is tender when pierced with a knife, 12 to 14 minutes.
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Meanwhile, toss chickpeas, arugula, radishes, lemon juice, and remaining 1 tablespoon oil in a bowl. Divide red pepper sauce among plates. Top with cauliflower steaks, salad, cheese, and almonds.