Fill a pot with water and place over high heat. Bring to a roiling boil.
In a microwave-safe dish, combine oil, garlic, chicken broth, and lemon juice. Add chicken and microwave on high for 1 minute and 30 seconds.
When water boils, add tortellini to pot and stir. When water returns to a gentle boil, add broccoli and stir. Stir occasionally until tortellini is done, approximately 8-11 minutes Drain tortellini and broccoli in a colander. Do not rinse.
Add sauce and chicken to pot. Add tortellini and 1/3 cup shredded cheese. Toss well to coat tortellini and broccoli and sauce.
To serve, divide pasta and sauce between 4 bowls. Garnish with remaining cheese. If desired, season with salt, pepper, and crushed red pepper.