Heat the oven to 350°F. In a Dutch oven or other large, heavy-bottomed pot, whisk together the millet flour and ½ cup olive oil. Place in the oven and bake, whisking every 20 to 30 minutes, until it turns the color of a roasted chickpea and has a nutty aroma, about 1 hour.

Meanwhile, cook the mushrooms: in a large cast-iron skillet, heat 1 tablespoon olive oil over medium heat. Add the shiitake mushrooms, cover, and cook, stirring occasionally, until fork-tender, 5 to 7 minutes. Transfer the mushrooms to a medium bowl.

Next, add 2 tablespoons oil to the skillet, and crank the heat up to high. Add the cremini mushrooms in one layer and cook, without stirring, until the mushrooms release their liquid, most of it evaporates, and the mushrooms start to brown, 2 to 3 minutes. Toss the mushrooms and cook for an additional minute or so, until browned on the second side. Transfer to the bowl with the shiitakes and season with salt.

Coat the bottom of the skillet with 2 to 3 more tablespoons oil. Without overcrowding, add portobello mushrooms in one layer and cook, still over high heat, until golden brown, about 2 minutes. Flip the mushrooms and cook until browned on the second side, 1 to 2 minutes. Transfer to a paper towel–lined plate and sprinkle with salt on both sides. Repeat with the remaining mushrooms, in batches, adding more oil when necessary.

To the now-empty skillet, pour in about ½ cup stock and bring to a rapid simmer while scraping the bottom of the skillet with a spatula to remove any browned bits. Pour back into the container with the remaining stock.

When the roux is ready, transfer the pot to the stove and place over low heat. Add the celery, green bell peppers, and onions  and cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes. Add the garlic and cook, stirring, until aromatic, 3 to 5 minutes. While whisking constantly, pour in the stock mixture and raise the heat to high. Continue to whisk while the mixture comes up to a boil. Add the tamari, bay leaves, cayenne pepper, and 1 teaspoon salt. Reduce the heat to medium-low and simmer until the gumbo is darkened in color, very thick, and flavorful, about 45 minutes.

Add the reserved shiitake and cremini mushrooms to the gumbo and simmer for 5 minutes, stirring occasionally. Add 3 tablespoons thyme and simmer for an additional minute. Season to taste with salt and pepper.

Serve the gumbo in shallow bowls with rice pushed to one side and the gumbo on the other, topped with the seared portobellos, and garnished with green onions, thyme, and a sprinkle of filé powder.