In a blender or food processor, pulse the cauliflower until the mixture has the consistency of rice.
Set a large heavy-bottomed skillet over medium-high heat. Add 2 tablespoons of the olive oil and heat to shimmering. Add the brown rice, cauliflower rice, turmeric and cayenne and stir to combine, then shake the skillet to spread the mixture out into an even layer. Cook, without stirring, until the bottom gets crispy, about 3 minutes. Sprinkle the garlic and ginger across the top and season with a pinch of salt and a twist of pepper. Remove from the heat, stir in the scallions and set aside.
Set a large nonstick skillet over medium heat. Add the remaining 1 tablespoon olive oil and heat to shimmering. Carefully crack the eggs into the pan and cook until the whites begin to brown around the edges, about 2 minutes. Add the cilantro and season with a pinch of salt and a twist of pepper. Remove from the heat, add 1 tablespoon water, cover and let steam for 30 seconds for runny yolks, 1 minute for medium-set yolks and 1 1/2 minutes for fully set yolks.
Place the brown rice and cauliflower on a plate, top with the eggs and serve with a lime wedge and hot sauce.
Make the brown rice: Fill a large pot with 10 cups water and bring to a boil. Add 2 cups brown rice and a couple pinches of salt and cook at a gentle boil, covered, for 30 minutes. Drain the rice and return it to the pot. Cover and let rest for 10 minutes. Remove the lid and fluff with a fork. Spread the rice out on a sheet pan and let cool before transferring it to an airtight container. Cooked brown rice will last up to 3 days in the fridge.