Start by cooking the rice. Bring a large pot of salted water to a boil. Once boiling, add the dry rice and cook for about 7 minutes, or until just tender. Drain and set aside, covered.
Prepare the curry: heat the oil in a medium pot or saucepan. Once hot, sautée the shallots, garlic, and ginger for a couple minutes. Add the red curry paste and sautée for another 2 minutes.
Add the mushrooms, carrots, red bell pepper, and cook for another 5 minutes.
Pour in the full-fat coconut milk, water, maple syrup, soy sauce, tomato paste, chili flakes, and salt. Bring to a boil and let simmer uncovered for about 20 minutes or until carrots are tender. Cover to keep warm.
While the curry is cooking, prepare the crispy rice. Mix about 1/2 cup of cooked rice with the vegan yogurt.
Melt the vegan butter and oil in a 7-inch clay pot or deep skillet (I personally used two 4.5-inch clay pans and divided the butter and oil) over low-medium heat.
Once the butter has melted, add the rice yogurt mixture to the pan and spread it into an even layer using the back of a spoon. Add the rest of the rice and slightly pack it down. Using a chopstick or the handle of a wooden spoon, make 4-5 holes in the rice. This will allow steam to escape.
Cook over low-medium heat for about 18 minutes, rotating the pan every 2-3 minutes by 1/8 of a turn. This will prevent the rice from browning unevenly.
Using a spatula or tablespoon, check the edges to see if the rice has developed a crust and if it's golden brown. Run the spoon around the edges of the pan, place a plate over the pan and carefully but quickly invert the rice cake over the plate. You should have a beautiful golden brown crust! Cut into 4-6 pieces.
To serve, divide the curry between 3 serving bowls and top with crispy rice pieces, fresh cilantro, and a squeeze of lime!
This red curry will keep for up to 3 days in the refrigerator. Crispy rice is best served the same day.