Melt butter in a medium saucepan over medium heat.

Add minced shallots to the melted butter and saute until softened, approximately 3 minutes.

Stir in flour, Italian seasoning, salt, and pepper to create a roux.

Cook the roux for 1 minute, stirring constantly to avoid burning.

Gradually add half-and-half and lemon juice to the roux, stirring continuously to prevent lumps.

Cook the sauce, stirring constantly, until it thickens and becomes smooth.

Gently stir in the cooked and drained broccoli florets until they are evenly coated in the sauce.

Serve immediately as is or as a side dish with chicken Kiev.