Preheat your oven to 190°C (375°F). Lightly grease a 23x33 cm (9x13 inch) baking dish with cooking spray or a small amount of olive oil.

If using fresh broccoli, wash and cut it into bite-sized florets. If using frozen, you can use it directly or thaw it slightly. Place the broccoli florets in a large pot, cover with water, and bring to a boil. Blanch for 3-4 minutes until bright green and slightly tender. Drain thoroughly and set aside. This par-cooking step ensures the broccoli is tender without becoming mushy in the bake.

While the broccoli is blanching, heat 15ml (1 tbsp) of olive oil in a large skillet or Dutch oven over medium heat. Add the finely chopped yellow onion and sauté for 5-7 minutes until softened and translucent. Add the minced garlic and cook for another minute until fragrant, being careful not to burn it.

Add the sliced cremini mushrooms and diced red bell pepper to the skillet with the onions and garlic. Add the remaining 15ml (1 tbsp) of olive oil. Cook for 8-10 minutes, stirring occasionally, until the vegetables are tender and the mushrooms have released their liquid and started to brown.

Sprinkle the 30g (0.25 cup) of all-purpose flour over the cooked vegetables in the skillet. Stir well and cook for 1-2 minutes to toast the flour slightly. This helps to thicken the sauce and cook out the raw flour taste.

Gradually whisk in the 500ml (2 cups) of milk, a little at a time, ensuring there are no lumps. Continue whisking until the sauce is smooth. Bring the mixture to a gentle simmer, stirring constantly, until it begins to thicken. This should take about 3-5 minutes.

Reduce the heat to low. Stir in the 150g (1.3 cups) of shredded sharp cheddar cheese and 50g (0.4 cup) of shredded Gruyere cheese. Continue stirring until the cheeses are completely melted and the sauce is smooth and creamy.

Stir in the 1 tsp (5ml) of Dijon mustard, 5g (1 tsp) of salt, 2g (0.5 tsp) of black pepper, and optional 0.5g (1/8 tsp) of freshly grated nutmeg. Taste the sauce and adjust seasonings if necessary.

Gently fold the blanched broccoli florets into the cheesy vegetable sauce. Ensure all the broccoli is well coated. Pour this mixture evenly into the prepared baking dish.

In a small bowl, combine the 50g (0.5 cup) of breadcrumbs with the 25g (0.25 cup) of grated Parmesan cheese. Sprinkle this mixture evenly over the top of the broccoli and cheese mixture in the baking dish.

Bake in the preheated oven at 190°C (375°F) for 20-25 minutes, or until the topping is golden brown and the bake is bubbly around the edges. The cheese sauce should be melted and heated through.

Remove the broccoli cheese bake from the oven and let it rest for 5-10 minutes before serving. This allows the sauce to set slightly, making it easier to serve.