Heat canola oil in a large skillet over medium-high heat. Add the onion, reduce heat to medium and cook 4-5 minutes or until beginning to soften. Add the garlic, ginger, turmeric, cumin, coriander and cayenne. Stir briefly (approximately 30 seconds) or until fragrant.
Add the vegetable broth, coconut milk, carrots and turnips. Bring to a boil, reduce heat to low, cover and simmer 15-20 minutes or until vegetables are tender.
Add the turnip greens in handfuls if necessary, allowing each to wilt. Season to taste with salt and black peopper.
Serve with brown basmati rice.
MAKE AHEAD: Can be made 1 day ahead of time. Refrigerate until needed. Reheat on the stovetop or microwave until heated through.FREEZER-FRIENDLY: Place in an airtight container and freeze 1-2 months. Thaw in the refrigerator or microwave. Reheat on the stovetop or in the microwave.