Snap off tough ends of asparagus. Remove scales with a vegetable peeler or knife, if desired. Cut asparagus diaonally into 1 1/2-inch pieces. Place asparagus pieces and broccoli flowerets in a vegetable steamer over boiling water; cover and steam 6-8 minutes or until vegetables are crisp-tender. Remove from heat; set aside.

Saute onion and garlic in oil in a large skillet until tender. Add carrot and chopped peppers to onion mixture; saute until crisp-tender. Remove heat; drain.

Combine whipping cream, broth, green onions, basil, and salt in a medium skillet. Cook over medium-high heat 5 minutes, stirring occasionally.

Cook linguine according to package directions. Drain well; place in a large serving bowl. Add reserved vegetables, whipping cream mixture, and sliced mushrooms; toss gently. Sprinkle with Parmesan cheese and pepper; toss gently. Serve immediately.