Preheat the oven to 400°F. Spread the carrot sticks, sweet potato cubes, red bell pepper strips, and zucchini half-moons on a baking sheet. Drizzle with 1 tablespoon olive oil and sprinkle with salt and pepper. Toss to coat.
Roast the vegetables for 20 minutes, turning once halfway through, until the edges turn golden and the pieces soften.
While the vegetables roast, add the chickpeas, pumpkin puree, tahini, garlic clove, remaining 2 tablespoons olive oil, lemon juice, cumin, smoked paprika, salt, and pepper to a food processor.
Blend the mixture until smooth, stopping to scrape down the sides as needed. Add a splash of water if the hummus feels too thick.
Spoon the hummus onto a serving platter and spread it into an even layer. Arrange the roasted vegetables around the hummus. Sprinkle the chopped parsley over the top before serving.