Combine the finely minced fresh basil, balsamic vinegar, lemon juice, Dijon mustard, honey, and extra-virgin olive oil in a jar with a tight-fitting lid or a small bowl. Shake thoroughly or whisk until the vinaigrette is well emulsified. Set aside 3 tablespoons for marinating the chicken and reserve the rest for dressing the salad.
If the chicken breasts are thick, slice them in half lengthwise to create thinner cutlets—this helps achieve even cooking and maximum flavor absorption. Place the chicken breasts and 3 tablespoons of the prepared vinaigrette in a shallow dish or zip-top bag, turning the chicken to coat it thoroughly. Cover and refrigerate to marinate for at least 20 minutes and up to 24 hours.
Preheat your grill, arranging it so there are areas of both direct and indirect heat. Remove the marinated chicken from the fridge, drain off excess marinade, and season both sides generously with kosher salt and ground black pepper. Grill the chicken over direct heat until noticeable grill marks form, then transfer to the cooler, indirect side and cook for another 4 to 6 minutes or until cooked through. Transfer the chicken to a cutting board and let it rest for 5 minutes before slicing thinly. I like to let the chicken rest—this makes it extra juicy when you slice it.
In a large salad bowl, combine the assorted salad greens, diced cucumbers, quartered strawberries (or substitute with other berries), thinly sliced basil ribbons, and crumbled feta cheese. Gently toss to distribute the ingredients evenly. For a more vibrant flavor, sometimes I add a few extra fresh basil leaves to the mix.
Arrange the grilled and sliced chicken on top of the prepared mixed greens. Sprinkle the candied sliced almonds over everything and drizzle with the remaining basil balsamic vinaigrette. Garnish with additional basil leaves if desired, and serve immediately for the freshest taste.