Preheat oven to 425°F (220°C)
Line a large baking sheet with parchment paper
In a large bowl, toss potato wedges with olive oil
Add garlic, oregano, thyme, lemon zest, paprika, salt, and black pepper
Toss until wedges are evenly coated
Arrange wedges in a single layer on baking sheet, cut side down
Roast until golden brown and crispy, flipping halfway through
Remove from oven and sprinkle with fresh dill and parsley
While potatoes roast, combine Greek yogurt, grated cucumber, olive oil, lemon juice, garlic, dill, salt, and pepper in a bowl
Stir until smooth and refrigerate until ready to serve
Serve hot potato wedges alongside chilled tzatziki sauce