Combine the tomatoes, onion, garlic, and 1 cup of the chicken broth in a blender and blend until completely smooth; strain through a fine mesh sieve if you prefer a velvety broth.
Heat the vegetable oil in a medium pot over medium heat. Add the fideo pasta and toast, stirring constantly, until deeply golden and fragrant, 3–5 minutes.
Carefully pour the blended tomato mixture into the pot and cook, stirring, until it reduces slightly, darkens in color, and loses its raw edge, 4–6 minutes.
Stir in the remaining chicken broth along with the kosher salt and ground black pepper. Bring to a boil over medium-high heat.
Reduce to a gentle simmer and cook uncovered, stirring occasionally, until the fideo is just tender but not mushy, 8–10 minutes; the noodles should be pliant and the broth lightly thickened.
Turn off the heat and let the soup rest for 3 minutes to settle and finish hydrating the noodles.
Ladle into bowls, garnish with chopped cilantro, and serve with lime wedges.