Heat a large Dutch oven or large heavy-bottomed pot over medium heat. Add 2 tablespoons of the olive oil and heat through.
Add the chicken and brown on all sides, about 4 to 5 minutes total. Remove the chicken from the pot and set aside.
Add the onion to the pot and sauté, stirring occasionally, until the onion is soft and tender, about 5 to 6 minutes.
Add the garlic and ginger, stirring, until fragrant, about 20 seconds. Stir in the green curry paste, and let cook until fragrant, about an additional 30 seconds.
Add the coconut milk and chicken, stirring to combine, and bring the mixture to a simmer.
Stir in the chicken broth then bring to a boil and cover the pot or Dutch oven and simmer over medium-low heat until the chicken is cooked through and tender, about 30 minutes.
Heat oven to 400ºF (200ºC). Toss the slices of sweet potato in the remaining olive then arrange in a single layer on an aluminum foil-lined baking sheet. Bake until the sweet potatoes are tender and the edges begin to brown, about 20 minutes.
Bring a medium pot of water over medium-high heat to a boil. Cook the rice noodles, stirring occasionally, until tender but not mushy, about 6 minutes. Drain in a colander under cold water, then divide the noodles among the serving bowls.
Remove the chicken from the pot and shred using two forks and return the chicken to the pot.
Stir in the fish sauce and mushrooms to the curry mixture. Return the mixture to a simmer and let cook for about 10 minutes. Add the sweet potato slices then remove from the heat.