Heat oil over medium-high heat in deep 10-inch skillet; add mushrooms, saute until lightly browned, about 5 minutes.
Add pork to skillet; saute until pieces are evenly browned, about 10 minutes.
Add squash, broth, salt and pepper; heat to boiling, reduce heat to low, cover and simmer 45 minutes, stirring occasionally.
In small bowl, combine cornstarch and water, stirring to blend thoroughly. Stir cornstarch mixture into skillet; add onions, heat to boiling; reduce heat to low and cook 15 minutes, stirring occasionally.
Stir broccoli into skillet, cover and simmer 5 to 10 minutes longer until all vegetables are tender.
If desired, top simmering stew with refrigerated biscuits after stirring in broccoli, cover and simmer until "dumplings" are cooked through.