Preheat the oven to 425°F (220°C). Toss broccoli and carrots with olive oil, salt, and pepper. Spread on a baking sheet and roast for 20-25 minutes until tender.

Boil potatoes in salted water until tender, about 15-20 minutes. Drain and return to pot. Add garlic, butter, milk, salt, and pepper. Mash until smooth.

In a large mixing bowl, combine mixed greens, cherry tomatoes, cucumber, and red onion. Drizzle with olive oil and balsamic vinegar, then season with salt and pepper. Toss to combine.