Bring the broth to a boil in a small saucepan and add the millet. Cover, reduce to a simmer, and cook until soft, 15-20 minutes. Transfer the cooked millet to a large bowl.

Heat 2 teaspoons oil in a nonstick skillet over medium heat. Add the shallot, carrot, garlic and thyme and cook 2-3 minutes until partially softened. Add the spinach and season it with a pinch of salt. Cook until wilted, another 2-3 minutes. Transfer the mixture to the bowl with the cooked millet and let it cool for a few minutes. Add ¼ teaspoon salt, the egg, and egg white and stir to combine.

Form the mixture into 12 patties (about 2 tablespoons each), compacting them well so that they hold together. Heat 2 teaspoons oil in the skillet over medium heat. Add half of the patties to the pan and cook until golden brown, about 4-5 minutes. Flip and cook another 4-5 minutes on the second side. Remove from pan. Heat the remaining 2 teaspoons oil and cook the remaining patties.

Serve millet cakes with Greek yogurt or your favorite dipping sauce.