In a large saucepan over medium heat, brown the ground beef. Once the beef is browned, add the onion and garlic. Cook until the onion is translucent, about 5 minutes. Add the salt, cumin, chili powder, cayenne, paprika, and oregano. Cook for 2-3 minutes more to allow the flavors to meld and ensure the beef is cooked through. Remove the beef mixture from the pan and set aside.
In a clean large saucepan over medium heat, combine the shredded chicken and crushed tomatoes. Add the salt, cumin, chili powder, cayenne, paprika, and oregano. Cook until warmed through, about 5 minutes. Remove from the pan and set aside.
In a medium bowl, mix together the Parmesan and Mexican-blend cheeses.
Heat a medium nonstick pan over medium heat. Add about ¼ cup (25 G) of cheese to the center of the pan and spread into a circle. Let the cheese melt, then add a spoonful of beef or chicken filling to the bottom of the circle.
Slide the cheese shell out of the pan onto a cutting board and let cool for 30 seconds, then roll tightly to encase the filling. The melted cheese should stick to the outside, sealing the taquito. Repeat with the remaining ingredients.
Serve the taquitos with lime wedges, sour cream, and fresh cilantro.