Heat olive oil in a pot over medium heat. Sauté the garlic, pepper, onion, and ginger for 2-3 minutes.
Add the broth, red curry, chicken, coconut milk, and brown sugar. Stir well, cover with a lid and bring to a simmer until the chicken reaches an internal temperature of 160°F using a thermometer.
In the meantime, cook the rice noodles according to the instructions on the package. Drain well and set aside.
Once the chicken is done remove it from the pot onto a cutting board, using two forks pulling in opposite directions pull the chicken apart until shredded. Then return it to the pot. Stir in the spinach and lime juice.
Stir in rice noodles. Taste and adjust the seasoning with salt and pepper as needed. Remove from the heat and portion. Garnish with cilantro. Serve immediately.