Bring the millet and 1 cup plus 1 tablespoon of water to a boil in a saucepan with a lid. Reduce the heat to low, and simmer, covered, for 15 minutes. Set aside.

Heat the olive oil in a medium sauté pan over medium heat. Add the onion and garlic and sauté, stirring frequently, for 2 minutes. Add the millet and salt and stir to combine. Remove from the heat, stir in the Parmesan cheese, let cool, and refrigerate until cold, at least 30 minutes.

Preheat the oven to 425°F. Remove the millet mixture from the fridge and stir in the egg. Chill the mixture in the freezer for 15 minutes. Shape 2 tablespoons of the mixture around 1 piece of cheese, completely covering the cheese, to form a thick patty. Season the breadcrumbs with salt and pepper and dredge the patties in the crumbs, pressing the crumbs into the patties to adhere them. Line a baking sheet with parchment paper. Place the patties on the sheet, then lightly coat them with baking spray. Bake for 15 minutes or until the patties are lightly toasted. Serve with dipping sauce, if desired.