In a large skillet, heat oil and butter and gently brown the garlic. Add broccoli and stir gently until pan gets very hot. Add chicken broth, cover and simmer just until broccoli is al dente.
Add half the fresh basil and the drained hot rigatoni, cooked al dente, to the skillet and mix thoroughly. Put on a hot serving dish and sprinkle with parsley, pepper, grated cheese, and remaining basil.
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