Slice the carrots into rounds. Wash the leek tops well (grit hides between the layers) and slice them thinly. Slice the ginger into coins.
Warm the garlic-infused oil in a large pot over medium heat.
Add the leek tops and carrots and cook, stirring, until softened, about 5 minutes.
Add the water, whole chicken breasts, thyme, ginger and salt. Bring to a boil over high heat, then reduce to low so it barely bubbles and simmer for 20 minutes, until the chicken reaches 74°C (165°F) in the thickest part.
Lift out the chicken onto a board and shred it with two forks. Fish out the ginger coins and discard.
Return the chicken to the pot, bring back to a simmer over medium heat, add the broken rice noodles and cook until tender, 4 to 5 minutes.
Season with black pepper, stir in the parsley and serve hot. Rice noodles soften as the soup sits, so for leftovers cook the noodles separately.
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Tips
Store-bought broth almost always has onion and garlic; making it this way avoids them.
Swaps
Storing and reheating
Keeps 4 days; noodles soften on standing, so freeze the soup without them.