Steam the broccoli until tender-crisp, drain and blot dry; chop any large pieces.

Boil the shells until just tender, adding carrot for the final minute, then reserve pasta water and drain.

Melt butter, whisk in flour for 1 minute, add both milks and simmer gently until lightly thickened.

Remove from heat and melt in American cheese, white cheddar and salt.

Fold in shells, carrot and broccoli and loosen with reserved pasta water as needed.