Preheat the oven to 425°F and line a large baking sheet with heavy-duty parchment paper.
Scrub the potatoes thoroughly under cold running water to remove dirt from the skins.
Cut each potato lengthwise into eight even wedges to ensure consistent cooking times across the batch.
Soak the cut wedges in a large bowl of salted cold water for at least 30 minutes to extract surface starch.
Drain the water completely and pat each wedge dry with a clean kitchen towel to ensure they crisp up in the oven.
Toss the dried wedges in a large mixing bowl with olive oil, salt, pepper, garlic powder, and smoked paprika.
Spread the wedges evenly on the prepared baking sheet and bake for 40 minutes, flipping halfway through to ensure even browning.
Sprinkle half the shredded cheese over the wedges during the last 10 minutes of baking.
Rinse the baking sheet, return the wedges (after removing residual cheese), and add a second layer of cheese if desired before repeating baking.
For the ranch dip, mash the avocado in a food processor. Combine with Greek yogurt, lemon juice, minced onion, minced garlic, dried dill, and dried mint. Pulse until smooth. Adjust seasoning if needed and refrigerate until ready to serve.