Cut potatoes into ½" dice. Cut olives into ¼" rounds across width. Cut shallot into ¼" rounds. Separate rounds into rings. Mince garlic. Cut mushrooms into ¼" slices.
Finish Preparing the Ingredients
Stem, seed, and cut red bell pepper into ½" dice. Halve grape tomatoes. Stem and coarsely chop basil. Rinse chicken breasts, pat dry, and season both sides with ½ tsp. salt and ¼ tsp. pepper.
Sear the Chicken
Heat a large non-stick pan over medium-high heat. Add chicken and 2 tsp.olive oil to hot pan and cook until browned, 3-4 minutes per side. Remove chicken to plate. Chicken will finish cooking in later step. Reserve pan; no need to wipe clean.
Start the Vegetables
Return pan used to sear chicken to medium-high heat. Add 2 tsp. olive oil and mushrooms to hot pan. Cook, stirring occasionally, until lightly browned, 3 minutes. Add potatoes, shallots, and red bell pepper to pan. Cook, stirring occasionally, until vegetables begin to soften, 5 minutes.
Finish Chicken and Vegetables
Add white wine and 1 ½ cups water to pan with vegetables. Cover and cook until potatoes are tender, 5-7 minutes. Once potatoes are tender, reduce heat to medium, and stir in olives, tomatoes, and garlic. Place chicken and any accumulated juices in pan, cover and cook until potatoes are soft and chicken reaches a minimum internal temperature of 165 degrees, 5-8 minutes. Add basil (reserve a pinch for garnish) and season with ½ tsp. salt and a pinch of pepper.
Plate the Dish
Scoop a serving of vegetables on a plate. Place chicken on top of vegetables. Garnish with remaining basil.