Place the Cotija, cilantro, olive oil, garlic powder, salt, and pepper in the bowl of a food processor or in a blender. Blend until well combined and all chunks are small. Add the avocado, and pulse until smooth (some small chunks of avocado are fine). Place avocado mixture in a bowl, and gently stir in chopped red onion and half of the chopped tomato (reserving the remainder for garnishing).
Place dip in a bowl, garnishing with remaining chopped tomato, additional cotija, and cilantro leaves if desired. Serve with tortilla chips, pita, veggies, or crackers.