In a large skillet over medium heat, cook the ground beef seasoned with black pepper, breaking it up as it cooks, until browned, about 5 minutes. Add the garlic, grated ginger, and chili paste, cooking for another minute. Stir in the peanuts and tamari, then bring the mixture to a simmer and cook until the sauce thickens and coats the beef, about 3-5 minutes. Mix in the shredded cabbage, Thai basil, and green onions, then remove from heat.
Warm one tortilla at a time in the microwave for 15 seconds. Spoon the beef mixture down the center, then sprinkle with chopped cilantro. Fold the tortilla over the filling, then fold in the sides and roll it forward. Repeat with the remaining tortillas and filling.
To prepare the peanut sauce, whisk together the roasted peanut oil, creamy peanut butter, rice vinegar, tamari, grated garlic, and chili flakes until smooth and well combined. Sprinkle the sauce with toasted sesame seeds and extra peanuts if desired.
Serve the wraps warm alongside the peanut sauce for dipping. For a complete dinner, serve with rice on the side.