Heat 2 1/2 tablespoons vegetable oil in a skillet over medium heat; add 1 1/2 tablespoons garlic and cook until golden brown, about 3 minutes.
Wash glutinous rice and jasmine rice in a bowl; rinse with water.
Heat remaining 2 1/2 tablespoons vegetable oil in a large saucepan; cook red onion, ginger, and 1 1/2 tablespoons garlic until aromatic, about 3 minutes. Add chicken and cook until brown, about 15 minutes. Stir in rice; cook 1 minute more. Season with salt and pepper. Pour in chicken stock. Bring to a boil; reduce heat and let simmer, stirring occasionally, about 5 minutes. Add more chicken stock if desired. Remove from heat.
Mix in fish sauce. Top with eggs, green onion, and remaining toasted garlic.