Cook pasta according to package directions; drain and keep warm. Sprinkle chicken with Cajun seasoning and cracked pepper; place in a lightly greased 13- x 9-inch pan.

Bake at 350° for 15 to 20 minutes or until done; cool slightly. Cut chicken crosswise into thin strips.

Combine 1 cup water and salt in a large skillet; bring to a boil. Add broccoli; cover and cook 3 to 4 minutes or until crisp-tender. Drain. Melt butter in skillet; add garlic, and saute until tender. Set aside 1 cup broccoli; add remaining broccoli to skillet, and cook 2 minutes.

Combine cornstarch and 1 1/2 tablespoons water in a bowl, stirring until smooth; stir in half-and-half. Gradually add to broccoli mixture.

Bring to a boil over medium heat, stirring constantly. Boil, stirring constantly, 1 minute. Stir in salt, peppers, and cheese. Spoon over pasta, and top with remaining 1 cup broccoli and chicken. Serve immediately.