Melt butter in a large nonstick skillet over medium-high heat; add onion. Cook, stirring occasionally, 8 minutes or until golden. Stir in mushrooms and next 4 ingredients; cook 5 minutes or until mushrooms are tender. Remove skillet from heat.
Bring chicken broth and 1/2 cup water to a boil in a medium saucepan; gradually stir in grits. Cover, reduce heat, and simmer, stirring occasionally, 5 minutes or until grits are thickened. Stir in portobello mixture and Parmesan cheese. Serve immediately.