Preheat oven to 375 degrees F. Line a sheet pan with aluminum foil.
Add the rice noodles to a bowl and cover with very hot water. Set aside to soak.
Heat oil in a skillet over high heat. Season chicken on both sides with salt and pepper. Add the chicken to the skillet and cook until chicken browns on one side. Flip chicken and repeat on the other side. Remove chicken to sheet pan and place in the oven. Bake until chicken is cooked through and reaches an internal temperature of at least 165 degrees F, preferably 180 degrees F, about 20 minutes.
When chicken is cooked through, remove from oven and transfer to a plate to rest. Shred with two forks.
Meanwhile, in the same skillet in which the chicken was browned, use a paper towel to remove excess grease. Add 1 can coconut milk to the skillet over medium-high heat and bring to a simmer. Add the red curry paste and brown sugar, stir, and reduce heat to a low simmer for about 5 minutes, stirring occasionally.
Drain softened noodles and add them to the skillet. They will still be slightly stiff and need a few minutes to cook. Stir the noodles into the sauce and continue to cook until the noodles soften. Add a little of the water the noodles were soaking in (or fresh water) if the sauce reduces too much and starts to get dry.
When the noodles are soft, adjust the salt to taste and stir in the shredded chicken. Top with sliced green onions and serve immediately. Offer Sriracha sauce for added spice if desired.