Place the chicken breasts in a small saucepan. Cover the chicken completely with water and place on the stove over medium high heat. Bring the water to 180 degrees F - just before the water starts to bubble. Poach the chicken until it reaches 165 degrees F.
While the chicken is poaching, in a medium saucepan over medium high heat, add the coconut milk, mushroom, broccoli, ginger, chili peppers, lemongrass, and the whites of the green onions and bring to a simmer.
Add the chili paste and simmer for 10 minutes.
Cool the chicken slightly and cut into 1 inch cubes. Add the cubed chicken to the soup.
Remove the lemongrass, ginger slices, and chili peppers with a slotted spoon and discard.
Add the cilantro, basil, and white pepper. Serve and garnish with lemon slices and green onion slices.
Save any leftover soup in an air tight container in the refrigerator for 3 to 4 days.