In a large mixing bowl, combine the broccoli florets, cauliflower florets, chopped red bell pepper, sliced yellow squash, and zucchini.
In a separate small bowl, whisk together the minced garlic, olive oil, dried oregano, smoked paprika, salt, and pepper.
Pour the garlic-oil mixture over the vegetables and toss them thoroughly until all the veggies are well-coated.
Spread the coated vegetables evenly on a large baking sheet lined with parchment paper, ensuring they are in a single layer for even roasting.
Roast the vegetables in the preheated oven for about 25-30 minutes, or until they are tender and slightly caramelized, stirring halfway through for even cooking.
Once done, remove from the oven and let them cool for a few minutes.
Transfer the roasted vegetables to a serving platter and garnish with freshly chopped parsley before serving.