While the vegetables are simmering, melt the butter in a small saucepan. Add the flour and whisk continuously for 1-2 minutes, until mixture starts to turn golden brown. Gradually whisk in the milk and continue to whisk until mixture has thickened, about 5 minutes. Add the cheese and stir until the cheese is melted and mixture is smooth.
Add the cheese mixture to the vegetables and stir until incorporated. If broccoli is not quite tender, continue to cook for another few minutes.
Use an immersion blender to blend soup to desired consistency. Alternatively, transfer soup to a blender to blend soup. Season to taste with additional salt and pepper. Serve with whole grain mustard croutons.