In a large skillet or wok, heat the 1 Tablespoon vegetable oil over medium-high heat. Add the 1 pound ground pork to the skillet and season generously with salt. Break it apart with a spatula and cook until browned and fully cooked, about 5 to 7 minutes.
While the meat is cooking, whisk together the 2 Tablespoons soy sauce, 2 Tablespoons hoisin sauce, 2 teaspoons chili paste, 1 teaspoon toasted sesame oil, and 1 teaspoon rice vinegar in a small bowl. Set aside.
Once the meat is browned, turn the heat down to medium and stir in the 1 small carrot matchsticks. Cook for 2 to 3 minutes until they begin to soften.
Stir in the minced 1 Tablespoon garlic and grated 1 teaspoon ginger. Sauté for about 1 minute until fragrant.
Add the 14 ounces coleslaw mix to the skillet and cook for another 2 to 3 minutes, stirring occasionally, until the vegetables are tender.
Pour the sauce mixture over the meat and vegetables. Toss everything together to coat evenly.
Cook for an additional minute or two to heat through and blend flavors. Serve hot, with garnishes like sliced green onion, wonton strips, and sesame seeds.