Preheat oven to 375° Fahrenheit. Wash 3 pounds red potatoes under running water, using vegetable brush or kitchen towel to remove all surface dirt. Dry washed potatoes well then place on cutting board.
Once all potatoes have been washed, carefully chop each potato into even, bite-sized pieces. Transfer chopped potatoes to large mixing bowl.
Pour ¼ cup neutral-tasting oil over potatoes in mixing bowl then toss or gently stir potatoes to coat fully in oil. Set bowl aside.
Add 1 tablespoon dried basil, 1 tablespoon dried oregano, 1 tablespoon onion powder, 1 tablespoon garlic powder, 1 tablespoon dried thyme, and 1 ½ teaspoons salt to small mixing bowl.
Stir well to thoroughly blend herbs, then pour approximately 25% of herb mixture into bowl of potatoes. Toss potatoes to distribute herbs, then add approximately 25% more herb mixture to bowl. Repeat as needed until potatoes are very well covered in oil and herbs. Note: entire herb blend may or may not be used.
Transfer herb-covered potatoes to large baking sheet and spread potatoes out across pan in single, even layer. Avoid overlapping potatoes if at all possible.
Place baking sheet in preheated oven. Roast potatoes 30 minutes, then carefully remove pan from oven.
Use spatula to flip all potatoes over once, so that tops of potatoes now face down. Return baking sheet to oven and roast potatoes 15 to 20 minutes more or until potatoes are golden brown and crispy. Note: Be careful not to burn potatoes - adjust times as needed depending on size of chopped potatoes.
Carefully remove baking sheet from oven. Transfer roasted potatoes to large heat-resistant bowl and set potatoes aside to cool 3 to 5 minutes.
While potatoes cool, add ⅔ cup full-fat mayonnaise, ⅓ cup chopped fresh cilantro, and ⅓ cup finely chopped red onion to medium mixing bowl. Stir ingredients together until well incorporated.
Once potatoes have cooled but are still very warm, scrape mayonnaise mixture into bowl of potatoes. Fold potatoes into mayonnaise mixture until completely coated.
Serve roasted potato salad immediately, either warm or at room temperature. Do not serve cold.