Combine millet, sweet potato, and broth in a medium pot. Bring to a boil, reduce heat, cover, and cook over medium heat until millet is tender and broth is absorbed, about 25 minutes. Turn off heat and let stand 5 minutes, covered.

Meanwhile, heat sesame oil in a large skillet; sauté mushrooms, tempeh, green onions, and garlic for 6–7 minutes, or until tempeh is browned. Stir in tamari and mirin; cook for 2 minutes, scraping up browned bits. Transfer to a dish and set aside. Wipe out skillet.

When millet mixture is done, mash with a potato masher. Stir in tempeh mixture until creamy and thick. Season with salt and pepper. When cool enough to handle but still very warm, quickly form into six patties.

Heat vegetable oil in skillet over medium heat and cook patties until lightly browned, about 3 minutes per side. Arrange on a platter and serve hot with garnishes.