Preheat the oven to 350˚ F. Lay the tostadas on a rimmed baking sheet and bake until toasted, about 5 minutes. Sprinkle with the chile-lime seasoning while still warm; set aside.
Heat the olive oil in a large nonstick skillet over medium-high heat. Add the carrot, garlic and a pinch each of salt and pepper. Cook, stirring occasionally, until the carrot is lightly browned, about 3 minutes.
Add the turkey and cook, breaking it up into small pieces with a wooden spoon, until no longer pink, about 5 minutes. Clear a space in the middle of the skillet and add the tomato paste, chili powder and cumin. Cook the paste mixture, stirring, until a shade darker, about 30 seconds, then stir the mixture into the turkey. Cook until well coated, about 1 more minute. Add 1/4 cup water and cook until saucy, about 1 minute. Remove from the heat and season with salt and pepper.
Spread the sour cream on the tostadas, then add the turkey. Top with lettuce, tomato, avocado and cheese.
To get extra veggies, add a grated carrot to ground meat dishes like we did here. You can also add grated carrots to meatballs, meatloaf and sloppy joes.