Heat olive oil in a large cast-iron or heavy-bottomed skillet over medium-high heat until shimmering.
Add the sliced mushrooms in a single layer and cook undisturbed for 3 minutes to allow browning.
Add the zucchini slices to the skillet and toss with the mushrooms.
Sauté the vegetables for an additional 5-7 minutes, stirring occasionally, until the zucchini is tender-crisp and browned.
Add the minced garlic, salt, pepper, and thyme; cook for 1 minute until the garlic is fragrant.
Remove from heat, garnish with fresh parsley, and serve immediately.