In a food processor, blender, or with an immersion blender, blend the carrot juice, one mashed avocado, ginger and coconut milk until smooth.
Reduce the heat to medium and pour the carrot juice and avocado mixture into the pan. Bring to a simmer. Simmer for a few minutes to reduce slightly. Stir in the red curry paste and lime juice. Stir in 2 tablespoons chopped cilantro. Turn off the heat.
In a small bowl, whisk the cornstarch into the room temperature yogurt. Slowly add a ladle full of the hot carrot broth into the yogurt mixture, whisking continuously. Then, off the heat, slowly pour the yogurt mixture into the carrot broth, whisking continuously. This tempering technique stabilizes the yogurt to keep it from curdling.
Add the chicken breasts and any accumulated juices back into the pan. Simmer at the very lowest heat for about 6-7 minutes, until the chicken is just cooked through. Season to taste with salt and pepper.
Serve the chicken and broth in a bowl with jasmine rice, and garnish with chopped avocado, remaining chopped cilantro, chopped peanuts, and toasted coconut, if desired. Drizzle with remaining avocado oil.