Heat oil in a large saucepan over medium heat. Add onions; cook and stir until softened, about 5 minutes. Add jalapenos; cook and stir until dark green, about 5 minutes. Remove from heat.
Heat broth in a saucepan over medium-high heat. Cook batches of ribeye slices in hot broth until medium-rare, 10 to 20 seconds per batch.
Bring a large pot of water to a boil. Add noodles; cook at a boil until tender, 3 to 5 minutes. Drain.
Place tortillas on a microwave-safe plate. Heat in the microwave until warm, 20 to 25 seconds.
Divide onion and jalapeno mixture, ribeye slices, noodles, chili-garlic sauce, bean sprouts, hoisin sauce, Thai basil, and cilantro among warmed tortillas. Spoon a small amount of broth on top. Fold opposing edges of tortillas over filling and roll up into burritos. Serve with lime slices.