Whisk vinegar and mustard in small bowl. Gradually whisk in oil; season dressing with salt and pepper.
Place chicken in large bowl. Warm drippings/butter in microwave just until melted. Drizzle over chicken; toss to coat. Add scallions, 1/3 cup almonds, and peppers and toss.
Add greens, basil, and dressing to bowl with chicken; toss to coat. Season chicken salad to taste with salt and pepper. Sprinkle remaining 3 tablespoons toasted almonds over and serve.