Heat 2 tablespoons of the oil in a large frying pan over medium-high heat. When the oil shimmers, add the ginger, half of the curry powder, and all of the cauliflower. Season with salt and cook, stirring occasionally, until fragrant and the cauliflower is golden brown, for about 6 to 8 minutes. Remove to a plate with a slotted spoon.

Wipe out the pan, return to the stove over medium heat, and add the remaining 1 tablespoon of oil. When it shimmers, add the onion, garlic, and chile (if using), season with salt, and cook until softened, about 3 minutes. Stir in the remaining curry powder, and cook until fragrant. Add the cauliflower, potatoes, and broth, and bring to a boil.

Decrease the heat to low, cover, and cook for 5 minutes. Remove the cover and stir through to coat all the cauliflower. Cover again and simmer until the potatoes are knife-tender, about 12 to 15 minutes. Remove the cover, add the black beans and the peas and cook until the peas are bright, about 3 minutes. Adjust the seasoning as desired, stir in the cilantro, and use to fill the burritos.

To make the burrito, place the curry in the middle of the flatbreads. Top with yogurt or sour cream and chutney or jam, fold in sides, then roll up into a burrito shape, and serve.