Prepare Tarragon Pesto: Add tarragon, parsley, 2 tbsp. pine nuts, 1 tsp. lemon juice, and shallots to a food processor; chop coarsely. With machine running, gradually add 3 tbsp. olive oil. Season to taste with salt and pepper. Add more olive oil, to thin, if necessary.
Prepare Lemon Vinaigrette: Whisk remaining 4 tsp. lemon juice and 3 tbsp. olive oil in small bowl. Season dressing with salt and pepper.
Heat grill or pan to medium-high heat. Brush chicken breasts on both sides with additional olive oil. Sprinkle with salt and pepper. Grill until grill marks form and chicken is cooked through, 7 to 8 minutes per side. Transfer to cutting board and let rest 5 minutes.
Using clean brush, brush both sides of bread with olive oil. Sprinkle with salt, pepper, and garlic powder. Grill (or toast in pan or oven) until toasted on both sides, about 1 minute per side. Cut toast slices diagonally into eighths.
Place greens, radishes, and cucumbers in large bowl. Toss with dressing. Season to taste with salt and pepper. Divide salad among 4 plates.
Cut grilled chicken breast halves crosswise into 1/3-inch-thick slices. Arrange 1 sliced chicken breast half atop each salad. Top with garlic bread triangles. Spoon tarragon pesto over salad and top with remaining pine nuts.
Recipe adapted from www.bonappetit.com