Toast almonds in a nonstick skillet over medium heat until golden.
Add sugar, butter, and salt, and stir until sugar dissolves and coats almonds. Transfer to a plate to cool.
Whisk vinegar, 1/4 cup raspberries, 2 T. honey, tarragon, shallots, and salt together in a bowl.
Drizzle in 1/4 cup oil, whisking constantly. Set 1/2 cup vinaigrette aside for marinating chicken; reserve remaining vinaigrette for tossing with the salad. Pound out chicken breasts in a large resealable plastic bag to 1/2" thick; marinate chicken in 1/2 cup vinaigrette, 15 minutes.
Combine 1 T. honey and 1 T. oil and brush onto peach halves. Remove chicken from marinade, season with salt and pepper, and grill until cooked through, 3–4 minutes per side.
Grill peaches until lightly marked, about 3 minutes per side.
Just before serving, toss mesclun with remaining vinaigrette, then serve over chicken.
Garnish with glazed almonds and remaining raspberries.
Raspberry Chicken with Grilled Peaches
Lightly toast the almonds, then glaze in butter and sugar. Remove from pan and let cool completely.
Combine vinaigrette ingredients, lightly crushing the raspberries with a whisk while adding the oil.
To prevent chicken from tearing, pound it out in a plastic bag with 1 teaspoon of water inside.
Because the chicken is so thin, be sure to watch it closely so it doesn’t overcook and dry out.