In a heavy bottom skillet or dutch oven over medium-high heat add oil and once hot saute onion until softened. Follow with garlic and ginger, salt, black pepper, veggies (except broccoli), red curry paste, and turmeric. Saute until veggies are slightly softened.
Stir in coconut milk, vegetable broth, and sugar, and reduce the heat to medium-low. Here you can add lemon grass or kaffir leaves if using.
Take it to a gentle simmer and cook until the sauce starts to thicken. Stir in broccoli (you can add broccoli along with the veggies in the beginning but I like my broccoli with a little crunch to it and bright green colored, personal preference!), kale, and snow peas, drizzle with lime juice, soy sauce.
Simmer until kale is reduced in size. Taste for seasonings once more.
The curry will start to thicken even more once it’s cooled. To reheat add a little vegetable broth or coconut milk.
Serve this curry with more lime juice, fresh Thai basil leaves (or regular basil) or cilantro, coconut shavings over cauliflower rice, jasmine rice (or any long grain rice), noodles, or simply with bread and shrimp crackers.