Start by preparing the vegetables. Wash and peel the parsnips. Cut off the root and leafy ends and discard. Chop the parsnips into 1/2-inch slices. Cut the cauliflower into 2-inch florets and rinse it under cold water.
Once water is boiling, add parsnips and cauliflower florets and let simmer for 25-30 minutes, or until the vegetables are fork tender.
Drain well and transfer to the bowl of a food processor. Add garlic and process until smooth, scraping down the sides from time to time.
Transfer the purée to a saucepan, stir in the vegan butter, maple syrup, sesame oil, and a pinch of nutmeg. Heat over medium heat, stirring constantly until the butter is melted and the purée thickens slightly, about 5 minutes. Taste and add more salt and/or pepper if needed. Cover to keep warm while you prepare the mushrooms.
Garlic Butter Mushrooms
Heat the vegan butter in non-stick skillet over medium heat. One hot, add garlic and cook for 1 minute. Add mushrooms and rosemary sprigs and continue to cook for 3-5 minutes, or until the mushrooms are soft and lightly browned.
In the meantime: In a small bowl, combine the white wine, water, soy sauce, and cornstarch. Stir until the cornstarch is dissolved.
Pour the wine mixture over the mushrooms and cook for another minute, or until the sauce has thickened. If it's not saucy enough, add 2-3 tbsp water. Remove from heat.
Transfer the mashed cauliflower and parsnips to a serving plate, top with the garlic butter mushrooms and garnish with chopped chives. Serve immediately. Alternatively, you can serve the purée and mushrooms on different plates.