Preheat the oven to 425°F (use convection if available) and line a baking sheet with aluminum foil for easier cleanup.
Place the chicken pieces, red onion chunks, whole mushrooms (stem/gill side up), and zucchini pieces in a large mixing bowl or directly on the prepared baking sheet.
Drizzle the olive oil over the chicken and vegetables, then sprinkle with paprika, dried oregano, kosher salt, and black pepper.
Toss everything thoroughly with your hands or tongs so the oil and seasonings coat the chicken and vegetables evenly.
Spread the chicken and vegetables in an even layer on the baking sheet and roast for about 20 minutes, or until the chicken is cooked through and the vegetables are tender; start checking at 15 minutes if pieces are small.
Optionally rotate the baking sheet halfway through roasting for more even browning.
Remove from the oven, garnish with the minced parsley if using, and serve immediately.