Start off by roasting the chicken breasts. Preheat the oven to 400°F. Rub chicken with olive oil and season generously with salt and pepper.
Roast for 30 to 40 minutes, or until cooked through. Set aside and let cool.
I like to blanch my sugar snaps and peas quickly. Bring a pot of water to a boil. Add the sugar snaps for 2 to 2 1/2 minutes. Add the peas for about the last minute.
Drain and immediately put the veggies into a bowl of icy cold water.
Add the lettuce, spinach, parsley, pepper, radishes, sugar snaps, peas, and carrots into a large salad bowl. Season with salt and pepper.
In a small bowl, whisk together vinegar, shallot, honey, and garlic. Slowly whisk in the olive oil.
Drizzle salad with dressing and toss well. Top with roasted chicken.