Heat a large pot of lightly salted water to boiling. Add pasta and cook 4 minutes. Stir in broccoli, return to a boil and cook for 3 minutes. Drain.
Meanwhile, in a small saucepan, heat milk just until bubbles begin to burst at edge of pan. Add cheese slices one by one, whisking until smooth. Simmer 3 minutes.
Transfer pasta and broccoli to a large bowl. Add cheese sauce and stir to combine. Let stand 5 minutes before serving.