In a medium saucepan, heat oil over medium heat. Add onion and garlic, and saute until golden brown.
In a small saucepan, stir together milk, chicken broth, flour, salt and pepper over low heat until smooth and thick. Stir into onion mixture. Continue to cook over medium low heat, stirring frequently, until the sauce is thick. Stir in Parmesan cheese.
Meanwhile, cook pasta in boiling water. Add broccoli to the pasta for the last several minutes of cooking. Continue cooking until the pasta is al dente.
Drain the pasta and vegetables, and transfer to a large bowl. Toss with sauce. Serve.