Mix together the fish sauce, rice vinegar, tomato paste, and sugar in a bowl and set aside.
Prepare the rice noodles according to package directions, keeping them slightly al dente.
Scramble the eggs in a skillet until fully cooked, then remove from the pan and set aside.
Add the canola oil to the hot skillet, then add the garlic, baby carrots, and mushrooms.
Cook for 2 to 3 minutes until tender and fragrant.
Pour in the prepared sauce and stir to combine.
Add the green onions, scrambled eggs, chicken, shrimp, and peanuts.
Cook and stir for about 2 minutes until heated through.
Add the cooked noodles and bean sprouts.
Toss everything together and cook for about 2 more minutes until well combined.
Transfer to plates and serve with lime wedges.
Sprinkle with crushed red pepper flakes if desired.