Bring a large pot of water to a boil; add broccoli and green beans. Simmer until vegetables are just tender, but still crunch, about 5 minutes. Drain.
Melt butter in a large skillet over medium heat; cook and stir mushrooms until they begin to soften, about 1 minute. Add baby corn and continue to cook and stir until heated through, about 1 minute more. Stir broccoli and green beans into mushroom mixture; season with Cajun seasoning and toss with olive oil.
