In a large pot, bring the chicken broth to a boil. Add the tomato paste, fish sauce, sugar, salt, and pepper. Reduce heat and simmer for 15 minutes.
While the broth simmers, cook the rice vermicelli noodles according to package directions. Drain and set aside.
In a separate pan, heat the vegetable oil over medium heat. Add the chopped onion and cook until softened, about 5 minutes. Add the minced garlic and cook for another minute until fragrant.
Add the crab meat to the pan and cook for 2-3 minutes, until heated through.
Add the crab mixture to the simmering broth. Bring to a gentle boil.
Divide the cooked rice vermicelli noodles among bowls. Ladle the crab noodle soup over the noodles. Garnish with bean sprouts and Thai basil leaves. Serve immediately with lime wedges.