Toast coconut in a small, dry skillet over medium heat, stirring, until golden. Set aside.
Rinse quinoa well in a fine-mesh sieve, then drain. Combine quinoa, 1 1/2 cups water, 1/2 cup coconut milk and 1/2 teaspoon salt in a medium saucepan and bring to boil over high heat. Reduce heat to low, cover, and cook until quinoa has absorbed the liquid, about 15 to 20 minutes. Remove from heat.
While the quinoa cooks, heat olive oil in a large skillet over medium-high heat. When it shimmers, add broccoli and cauliflower and cook, stirring frequently, about 2 minutes. Then toss in carrots and cook about a minute longer.
Add celery, scallions, ginger, and garlic and cook, stirring often, until fragrant, about 2 minutes. Place tomatoes in the skillet and mix well. Add parsley, mint, smoked paprika and Aleppo pepper and stir once or twice, until everything is heated through and combined. Season with salt and pepper.
Spoon quinoa into a wide bowl. Add vegetables and coconut flakes and mix well. Serve hot.