Cook the broccoli florets in boiling water for 5-10 minutes until al dente, then drain well and pat dry with paper towels.

In a large pot over low heat, melt the butter, then whisk in the flour and salt until smooth. Gradually add the milk, whisking constantly until the mixture thickens and begins to boil. Remove from heat.

Gently fold in the shredded cheese and broccoli until the cheese starts to melt. Stir in the beaten eggs until well combined.

Transfer the mixture to the prepared baking dish and bake for 30-45 minutes until set and lightly browned. Let it rest for 5 minutes before serving.