Preheat oven to 400°F and line a baking sheet with parchment paper.
Peel and dice the carrots and parsnips into 1-inch chunks.
Toss the vegetables with olive oil, dried oregano, and half of the sea salt and black pepper.
Spread the vegetables in a single layer and roast for 25 minutes until tender and slightly caramelized.
While roasting, place eggs in a medium saucepan and cover with one inch of cold water.
Bring to a rolling boil, then remove from heat, cover, and let sit for 9 minutes.
Transfer eggs to an ice bath for 5 minutes before peeling and slicing them in half.
In a small bowl, whisk together the Greek yogurt, fresh dill, lemon juice, and the remaining salt and pepper.
Plate the roasted root vegetables with the halved eggs and serve with the herb dip on the side.