If using wooden skewers, soak them in water for at least 30 minutes before grilling to prevent burning.
In a large bowl, whisk together olive oil, minced garlic, thyme, smoked paprika, salt, and pepper.
Add the mushrooms and zucchini chunks to the bowl and toss gently to coat evenly with the marinade. Let sit for 15-20 minutes.
Preheat your grill to medium-high heat (around 400°F).
Thread the mushrooms and zucchini pieces onto skewers, alternating between the two vegetables.
Place the skewers on the preheated grill and cook for 4-5 minutes per side, or until the vegetables are tender and have nice grill marks.
Remove from heat and let rest for 2-3 minutes before serving.