Place 2 pounds chicken breasts on a baking sheet. Season both sides with salt, pepper, and garlic powder. Bake at 375°F for 20–25 minutes until internal temperature reaches 165°F (use a meat thermometer inserted into the thickest part). The chicken should be no longer pink inside and juices should run clear. Let cool for 10 minutes on the pan.
Once cooled completely (about 15 minutes), cut chicken into bite-sized pieces, roughly 1/2-inch cubes. Set aside in a large mixing bowl.
In a medium bowl, combine 1 cup mayonnaise, 1/4 cup fresh lemon juice, and 2 tablespoons Dijon mustard. Whisk together for 1–2 minutes until smooth and well combined. The dressing should be creamy and pale yellow.
Add the dressing to the bowl with diced chicken. Gently fold to coat all pieces evenly (1–2 minutes). Don't overmix or the chicken will break apart.
Add 1/2 cup diced celery, 1/4 cup diced red onion, 1/4 cup chopped fresh dill, 1/4 cup chopped fresh parsley, 1/2 cup diced cucumber, 1/4 cup sliced almonds, and 2 tablespoons drained capers to the chicken mixture. Fold gently for 2–3 minutes until evenly distributed.
Taste the salad and season with additional salt and pepper as needed (1/4 teaspoon increments). Checkpoint: You are ready to serve when the chicken is evenly coated, vegetables are distributed throughout, and flavors taste bright and balanced.
To serve, divide 6 cups mixed leafy greens among plates or bowls. Top each portion with about 3/4 cup of the chicken salad mixture (or about 1 1/2 cups for a larger serving).
Drizzle each serving with 1/2 tablespoon extra virgin olive oil. Serve immediately, or cover and refrigerate for up to 2 hours before serving. The salad will stay fresh in an airtight container for up to 4 days.