Add olive oil and 1/2-tablespoon butter to a large skillet and set over medium-high heat.
Add zucchini slices to the hot oil; season with salt and pepper and cook for 3 to 4 minutes, or until fork-tender. Remove zucchini from skillet and set aside. If there's any liquid in the skillet, wipe it out.
Return skillet to the burner and add remaining butter; melt butter over medium-high heat.
Stir in the onions and cook for 2 minutes, or until just softened.
Add mushrooms and cook for 5 to 7 minutes, or until tender and nicely browned. Stir occasionally.
Stir in garlic and herbs; cook for 20 seconds.
Return zucchini to the skillet and mix with the mushrooms; cook for 1 minute, or until heated through.
Pour in the vegetable broth and cook for 2 minutes.
Taste for salt and pepper and adjust as needed.
Remove skillet from heat.
Sprinkle with parsley and parmesan; serve.