This story begins just as the great Sophia Petrillo began so many of hers on "Golden Girls." Picture it: Sicily, 1922. A down-at-the-heels chicken farmer wants to win the affection of a fetching young neighbor with a home-cooked meal. But it turns out she's paleo! What's a shabby chicken farmer to cook for this protein-preferring person that's still delicious enough to impress? He serves forth a pan-roasted chicken with a fragrant herb blend next to mozzarella-crusted Roma tomatoes and roasted green beans dappled with fresh garlic. The drizzle of sweet-tangy balsamic glaze clinched it, and the two lived together happily for many years, until they separated because one wouldn't stop talking about CrossFit.
Trim ends off green beans. Halve Roma tomatoes lengthwise. Use an half teaspoon measuring spoon to scoop out a ½" deep well in each tomato half. Mince garlic. Stem and mince parsley. Combine butter and half the parsley (reserve remaining for garnish) and a pinch of pepper in a small bowl. Rinse chicken, pat dry, and season both sides with half the Italian seasoning (reserve remaining for tomatoes), ¼ tsp. salt, and a pinch of pepper.
Cook the Tomatoes
Place tomato halves, cut side up, on one half of prepared baking sheet. Divide parsley-butter between each tomato well and top each with shredded mozzarella. Sprinkle mozzarella with remaining Italian seasoning, ¼ tsp. salt, and a pinch of pepper. Bake until cheese has mostly melted, 10 minutes. While tomatoes bake, sear chicken.
Sear the Chicken
Heat 2 tsp. olive oil in large oven-safe non-stick pan over medium heat. Add chicken breasts to hot pan and cook until golden brown, 2-3 minutes per side. Chicken will finish cooking in later step. While chicken cooks, toss green beans.
Toss the Green Beans
Toss green beans with garlic, ¼ tsp. salt, and a pinch of pepper in a medium mixing bowl.
Finish the Chicken
After tomatoes have roasted 10 minutes, remove baking sheet from oven. Place green beans on other half of baking sheet and spread into a single layer. Place baking sheet and pan with chicken in oven and bake until chicken reaches a minimum internal temperature of 165 degrees and cheese is brown and bubbly, 6-8 minutes. Rest chicken 5 minutes.
Plate the Dish
Place a serving of green beans on a plate. Add two tomato halves on plate, followed by a chicken breast. Garnish chicken and tomatoes with remaining parsley and drizzle balsamic glaze on chicken.