1. Rinse the bulgur wheat under cold water to remove any impurities.
2. In a medium saucepan, bring 200 ml of water to a boil. Add the rinsed bulgur wheat, reduce the heat to low, cover, and simmer for about 12-15 minutes or until the water is absorbed and the bulgur is fluffy. Remove from heat and let it sit for 5 minutes, then fluff with a fork.
3. Meanwhile, steam or boil the green beans in a separate pot for 5-7 minutes until tender but still crisp. Drain and let cool slightly before chopping them into small pieces appropriate for your toddler.
4. Preheat the oven to 180°C (350°F).
5. In a mixing bowl, beat the egg and add the cooked bulgur, chopped green beans, and olive oil (or butter, if using). Season with a pinch of salt and dried herbs if desired. Mix until well combined.
6. Prepare a small baking dish by lightly greasing it with a bit of olive oil or butter. Spoon the mixture into the dish, pressing it down gently to form an even layer.
7. Bake in the preheated oven for 20-25 minutes or until the top is slightly golden and set. Allow it to cool slightly before cutting it into small, manageable pieces for your toddler.
8. Serve warm and watch your toddler enjoy their nutritious breakfast!

Summary: This Green Bean and Egg Bulgur Bake is a wholesome and nutritious meal for toddlers over 10 months, providing a good mix of protein from the egg, fiber from the green beans, and carbohydrates from the bulgur wheat. It's easy for babies to pick up and eat, supporting their self-feeding skills. Store any leftovers in an airtight container in the fridge for up to 3 days. Ensure to check for common allergens, and adapt the recipe if your child has any specific dietary restrictions. Always supervise your child while eating to minimize any choking hazards.