Put enough chicken broth into a large sauté pan to cover the chicken breasts(amount of broth will depend on the size of your chicken breasts). Bring the the broth to a boil and reduce the heat to a simmer, add the chicken breasts. Poach for 15-20 minutes of until cooked through.
Make the dressing by combining the lime juice and mustard into a small/medium bowl and slowly whisk in the olive oil, salt, pepper, cream and herbs. Set aside.
Steam the asparagus spears for about 5 minutes. Remove and spread the spears out to cool. Add the frozen peas and steam for 2-3 minutes. Remove the peas and cool.
Cut the chicken breasts diagonally into thin slices. In a medium bowl, toss the peas, radishes, and asparagus with half of the dressing.
To Serve: Divide the vegetables between 4 plates. Place the chicken slices on top and spoon the rest of the dressing on top. Garnish each plate with dill sprigs and mint leaves.