Bring a large pot of salted water to a boil. Add your choice of 8 oz pasta and cook according to the package instructions until al dente. Drain and set aside, reserving about ½ cup of pasta water for later.
Heat 1 tablespoon of coconut oil in a large skillet over medium-high heat. Add the diced chicken breast and cook until golden and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add a bit more coconut oil if needed. Toss in the sliced red bell pepper and snap peas. Sauté for 3-4 minutes until tender-crisp.
Lower the heat to medium. Add minced garlic and grated ginger to the skillet, stirring for about 1 minute until fragrant. Stir in 1 tablespoon red curry paste and cook for another minute to release its flavors.
Pour in the entire can of coconut milk, stirring to combine with the curry paste. Add 1 tablespoon soy sauce and 1 tablespoon brown sugar. Simmer for 5-7 minutes until the sauce thickens slightly.
Return the cooked chicken to the skillet. Add the drained pasta and toss everything together to coat evenly with the sauce. If the sauce feels too thick, add reserved pasta water a tablespoon at a time until you reach your desired consistency.
Remove from heat and sprinkle with fresh cilantro. Serve immediately with lime wedges on the side for squeezing over the pasta.