Heat 1 tablespoon oil in a large saucepan over medium-low heat. Add onion and cook, stirring, until softened, 2 to 4 minutes. Stir in millet and garlic and cook, stirring, until fragrant, about 30 seconds. Add water and salt and bring to a boil over medium heat. Reduce heat to low, cover and cook, stirring once or twice, for 20 minutes. Stir in zucchini, carrot, Parmesan, thyme, lemon zest and pepper. Cook, uncovered, maintaining a simmer and stirring often to keep the millet from sticking, until the mixture is soft, very thick and the liquid has been absorbed, about 10 minutes more. Remove from the heat and let stand, covered, for 10 minutes. Uncover and let stand, stirring once or twice, until cool enough to handle, about 30 minutes.

With dampened hands, shape the millet mixture into 12 cakes or patties, 3-inch diameter (a scant 1/3 cup each).

Coat a large nonstick skillet with cooking spray and heat over medium heat. Add 4 millet cakes and cook until the bottoms are browned, 3 to 5 minutes. Carefully turn the cakes with a wide spatula and cook until the other side is browned, 3 to 5 minutes more. Coat the pan with cooking spray again and cook the remaining cakes in batches, reducing the heat if necessary to prevent burning.

Note: Millet, a small round golden-hued grain, is sustenance for much of the world's population. In the U.S. it is most often used as bird feed, but it is the most-consumed grain in India and is also widely eaten in Africa, South America, China and Russia. Millet provides some protein, B vitamins, fiber and trace minerals, such as magnesium and copper. Look for it in bulk bins at well-stocked supermarkets and natural-foods stores.

MAKE AHEAD TIP: Prepare through Step 1 up to 2 hours in advance.