Preheat your oven to 400℉ (220℃). Line a baking sheet with parchment paper.
Toss carrots, asparagus, and broccolini with olive oil, salt, pepper, garlic powder, and paprika. Spread evenly on the baking sheet.
Roast in the oven for 20–25 minutes, flipping halfway, until golden and tender with a slight crisp on the edges.
While veggies roast, mix Greek yogurt, grated cucumber, garlic, olive oil, lemon juice, fresh dill, and salt in a bowl. Chill until ready to serve.
Spread a generous layer of tzatziki on a serving plate or shallow bowl. Top with warm roasted veggies.
OPTIONAL GARNISH: Drizzle with olive oil, sprinkle with extra dill or crushed red pepper flakes, and serve with pita or crusty bread if desired.