Cook pasta in large saucepan as directed on package, omitting salt and adding broccoli to the boiling water for the last 2 min.
Meanwhile, heat oil in large skillet on medium-high heat.
Add sausage; cook on medium heat 5 min., stirring occasionally.
Add peppers; cook and stir 5 min. or until peppers are crisp-tender and sausage is done.
Drain pasta mixture.
Add to skillet along with broth, half-and-half and oregano; cook and stir 3 to 5 min. or until sauce is slightly thickened. Top with shredded cheese; cook 1 to 2 min. or until cheese is melted.