In a bowl, mix rice, carrots, onions, cheese, and thyme, add salt and pepper, to taste. Sprinkle baking powder and flour over mixture, then stir well. Pour in eggs and mix lightly until blended.

Heat a cast-iron frying pan over a fire or over medium-high heat. Add a thick film of oil. Drop 3 or 4 heaping spoonfuls of batter into pan and flatten slightly, making cakes about 3-inches in diameter. Cook until crispy and well browned on bottom (about 3 minutes), turn cakes with a spatula, and cook until browned on the other side (about 2 minutes). Drain on paper towels. Repeat with remaining batter, adding more oil as necessary. Serve hot.