Start the brown rice cooking first, since it takes long to cook. Rinse the rice several times, then drain it well. Put the ghee or coconut oil into the pot you will cook the rice in and heat it over medium-high heat. Add the drained rice and cook it, stirring constantly, until it is dry and heated. Crush the cardamom pods with the bottom of a glass and remove the little black seeds. Add them to the rice (discard the outer pods). Add the bay leaf, cinnamon stick, salt, and water. Bring to a boil, then stir the rice to loosen any that is stuck to the bottom. Reduce the heat to low, cover the pot with a lid, and let the rice simmer for 45 minutes undisturbed. When the time is up, turn off the heat and leave the lid on so the rice can steam and stay warm until it is time to serve it. Remove the cinnamon stick and bay leaf and fluff up the rice before serving.
Make the dal: Thinly slice 4 or 5 of the smallest button mushrooms. Chop the rest into pea-sized pieces. Set them aside.
In a small dutch oven or heavy bottomed saucepan, heat the ghee or coconut oil over medium high heat. Add the chopped onion and cook for 2 to 3 minutes, until the pieces just start to get translucent. Add the garlic, curry powder, turmeric, and red pepper flakes and cook for 2 to 3 more minutes. Then add the chopped and sliced mushrooms. Cook for 5 minutes.
Add the red lentils, water, salt, and pepper. Bring everything to a simmer, stir, then cover the pot and let it simmer for 40 to 45 minutes. Lift the lid and stir occasionally. Cook until the lentils are soft and the dal is a creamy thick texture. If you like your dal looser, add a bit more water, if you like it thicker, cook it for a few more minutes uncovered.
About 5 minutes before the dal is done, prepare the tarka: In a small heavy skillet or pot, melt the ghee or coconut oil over medium-high heat. When it is rippling, add the cumin seeds, coriander seeds, and mustard seeds. Cook until you can hear the seeds starting to pop. (A mesh splatter screen on top helps contain them, or a lid set loosely to the side over the skillet.) Shake the skillet and let the seeds pop for about 5 seconds, then immediately remove it from the heat. Stir in the turmeric and salt. Scrape the seeded oil into a small serving bowl.
When the mushroom dal is done, drizzle a little of the spice oil over the dal in the serving dish, and serve the rest for diners to drizzle over their individual servings on their plates. Serve the mushroom dal with the brown rice and the spiced oil.