Heat the oil in a large saucepan over moderate heat.
Add the garlic and simmer until fragrant, stirring often to prevent browning.
Add the broccolini and mushrooms and toss to coat. Simmer over moderate heat until tender, approx. 5-7 minutes. Add a tad more oil if your pan dries out.
Once the veggies are tender, bring heat to low.
Add the zucchini and carrots, stir to mix, and cover pan to keep warm.