Cook chicken & broccoli: Melt 1 Tbsp butter in a skillet. Sauté cubed chicken until cooked; season and set aside. Steam or boil broccoli until tender; drain and set aside.
Cook onions: Melt remaining butter in skillet. Sauté onions until translucent; season lightly.
Add mushrooms & garlic: Stir in mushrooms and garlic; sauté 2–3 minutes until fragrant.
Combine vegetables: Add cooked potatoes and broccoli; season and warm through.
Make custard: Whisk eggs, milk, cottage cheese, thyme, rosemary, chives, salt, and pepper until smooth.
Prepare bread: Grease baking dish. Toss cubed bread with melted butter.
Layer pudding: Spread half the bread in dish, top with half the chicken, vegetables, and cheese. Repeat with remaining ingredients.
Add custard: Pour custard over layers; press bread gently to absorb.
Rest & preheat: Let sit 15 min (or cover and refrigerate up to 12 hours). Preheat oven to 180°C (350°F).
Bake & serve: Bake 40 min until custard is set and top is golden. Rest 10 min. Serve warm with chopped chives or green onions.