For the pickle: Combine the carrot, chile, rice wine vinegar, fish sauce, sugar, brown sugar and sambal in a pint container. Shake to combine. Let sit for 1 hour.
For the broth: Coat a small stockpot with canola oil and bring to medium heat. Add the garlic, ginger and scallions, and sweat until aromatic, 5 to 6 minutes. Add the chicken stock, fish sauce, star anise and cinnamon. Bring to boil, then reduce to simmer and cook for 15 minutes.
Place chicken breasts in the broth and poach until cooked through, 8 to 10 minutes. When fully cooked, remove from broth and slice thinly on the bias. Set aside. Strain the broth.
Blanch and shock in an ice water bath first the sugar snap peas and then the noodles. Set aside.
To assemble: Place the noodles in a bowl and top with chicken. Garnish with sugar snap peas, pickled vegetables, chopped peanuts, basil and mung beans. Gently pour broth into the bowl. Add a squeeze of lime juice and enjoy!