Heat your grill on high for at least 10 minutes.
In a bowl or on a baking sheet, add the chicken and bell pepper slabs. Drizzle all over with the oil and sprinkle with salt and pepper. Use your hands to toss to coat well.
Once the grill has heated up, arrange the chicken and peppers on the grates, cover, and grill for about 4 minutes or until the meat easily releases from the grates. Flip and repeat, taking the peppers off early if they are nicely charred. Transfer everything to a cutting board to cool off a bit.
Meanwhile, add all chimichurri ingredients to a high-speed blender and blend starting on low and increasing to high until smooth.
Chop the chicken and the peppers into bite-sized pieces, then add to a large bowl. Add the beans, scallions, and chimichurri. Toss to coat well.
Serve the salad on its own or with any of the serving suggestions. Top with cheese and black pepper.