If using wooden skewers, soak them in water for at least 30 minutes.
Preheat the oven to 425°F. Line a large rimmed baking sheet with parchment paper.
Cut the bell peppers, zucchini, squash, and red onion into 1 to 1½-inch pieces.
Leave small mushrooms whole and cut larger mushrooms in half.
Whisk together the olive oil, lemon juice, garlic, Italian seasoning, smoked paprika, salt, and black pepper.
Place the vegetables in a large bowl. Add the marinade and toss until evenly coated.
Let the vegetables rest for 15 minutes.
Thread the vegetables onto the skewers, alternating the different varieties and leaving a little space between each piece.
Arrange the skewers in a single layer on the prepared baking sheet.
Roast for 20–25 minutes, turning halfway through, until the vegetables are tender and lightly browned.
Sprinkle with fresh parsley and serve with lemon wedges.
