Place the potatoes into a large pot and cover with salted water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, 8 to 10 minutes.
Drain and allow to steam dry for a minute or two.
Place potatoes in a large bowl.
Heat a large skillet over medium-high heat; grease with cooking spray. Cook and stir the green beans and onion until tender, about 5 minutes. Stir in the garlic; cook and stir until garlic is fragrant, about 1 minute more.
Transfer the green bean mixture into the large bowl with the potatoes.
Add the balsamic vinaigrette, roasted red peppers, and basil; toss lightly. Stir in the goat cheese.
