Remove the butter from the refrigerator to soften. Place an oven rack in the center of the oven; preheat to 450°F. Wash and dry the fresh produce. Snap off and discard any stem ends from the green beans. In a bowl, combine the breadcrumbs, cheddar and monterey jack, mayonnaise, and pesto. Season with salt and pepper; stir to combine.

Pat the chicken dry with paper towels. Season on both sides with salt and pepper. Transfer to one side of the tray. Evenly top with the cheesy breadcrumbs. Add the green beans to the other side of the tray. Drizzle with olive oil; season with salt and pepper. Toss to coat and arrange in an even layer. Bake, uncovered, 20 to 22 minutes, or until the green beans are tender when pierced with a fork and the chicken is cooked through.* Remove from the oven. Top the baked green beans with the softened butter. Carefully toss to coat. 

*The USDA recommends a minimum safe cooking temperature of 165°F for chicken.

Meanwhile, place the potatoes in a microwave-safe bowl. Drizzle with olive oil and season with salt and pepper; toss to coat. Cover the seasoned potatoes with a damp paper towel, tucking the edges of the paper towel around the potatoes. Microwave on high 9 to 12 minutes, or until tender when pierced with a fork. To the bowl of cooked potatoes, add the sour cream. Using a fork or potato masher, carefully mash to your desired consistency. Taste, then season with salt and pepper if desired. Serve the baked chicken and finished green beans with the mashed potatoes. Enjoy!