Warm 2 tablespoons avocado oil in a large pot over medium heat. Add the dry fideo and onion piece. Stir often until the noodles are lightly golden in patches.

Stir in the tomato sauce and cook for 1 minute. Add the chicken broth, chicken base, tomato bouillon, oregano, and cilantro. Bring to a boil, then reduce to a gentle simmer and cook about 10 minutes, until the noodles are tender. Remove the onion and taste before adding salt.

Warm the corn tortillas until pliable. Divide the cooked shredded chicken and crumbled queso fresco among them, then roll each tightly.

Pour enough avocado oil into a skillet to lightly coat the bottom. Fry the taquitos seam-side down over medium heat, turning until golden and crisp. Drain on a rack or paper towels.

Ladle the soup into bowls. Serve the taquitos alongside, with crema, extra queso fresco, and avocado to taste.