Preheat the oven to 425°F (220°C). Line a large sheet pan with parchment paper or lightly grease it.
In a large bowl, combine the sliced red bell pepper, yellow bell pepper, zucchini, and cherry tomatoes. Drizzle with 2 tablespoons of olive oil and sprinkle with half of the minced garlic, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and 1/2 teaspoon dried oregano. Toss to coat evenly.
Spread the vegetables evenly on the prepared sheet pan and roast in the preheated oven for 8 minutes.
While the vegetables roast, in the same large bowl, combine the shrimp with the remaining 1 tablespoon olive oil, the remaining minced garlic, smoked paprika, crushed red pepper flakes, remaining dried oregano, lemon zest, and lemon juice. Toss to coat the shrimp well.
Remove the sheet pan from the oven and add the seasoned shrimp on top of the partially roasted vegetables in a single layer.
Return the sheet pan to the oven and roast for an additional 4 minutes, or until the shrimp are pink and opaque and the vegetables are tender.
Remove from the oven and sprinkle with chopped fresh parsley before serving.