Prepare the cheese sauce first.

Melt butter in a medium saucepan over medium-high heat.

Add finely chopped onion and cook until softened, being careful not to brown them.

Stir in flour and cook for 1 minute, stirring continuously to create a roux.

Remove the saucepan from the heat and season the mixture with salt and white pepper.

Gradually add milk while stirring constantly to ensure a completely smooth mixture.

Return the saucepan to the heat and continue cooking, stirring, until the sauce thickens.

Reduce the heat to low and simmer for 3 minutes, stirring constantly.

In a small bowl, beat the egg yolk.

Stir about half of the hot cheese sauce into the beaten egg yolk, mixing well to temper the egg.

Pour the egg yolk mixture back into the saucepan with the remaining cheese sauce.

Add shredded swiss cheese to the sauce.

Cook over low heat, stirring constantly until the cheese is completely melted and the mixture has thickened further.

Be careful not to let the sauce boil.

Preheat the oven to 375°F (190°C).

Grease a 9x13 inch baking pan with butter or cooking spray.

Microwave the frozen broccoli stems until they are almost fully cooked but still slightly firm.

Rinse the fish fillets and pat them dry with paper towels.

Cut the fillets into two or three pieces depending on their size.

Brush the fish fillets with fresh lemon juice and sprinkle with salt and pepper.

Arrange the partially cooked broccoli spears in the bottom of the prepared baking pan.

Top the broccoli with the seasoned fish fillets.

Pour the cheese sauce evenly over the fish and broccoli.

Sprinkle the remaining 1/4 cup of shredded swiss cheese over the sauce.

Bake in the preheated oven for 20 to 25 minutes, or until the fish is cooked through and flakes easily with a fork.

For the last few minutes of baking, briefly broil the top until it is lightly browned, watching carefully to prevent burning.