Let’s start with the chicken, shall we? Using the bottom of a mason jar or wide glass, lightly pound your chicken breasts to an even thickness. Season both sides of the chicken with salt and pepper.
Heat a large sauté pan over medium-high heat. When hot, add 1 tablespoon olive oil and swirl to lightly coat the bottom of the pan. Lower the heat to medium and add the chicken breasts. Cook for 1 minute and then flip the breasts over. Reduce the heat to low, cover the pan with a tight-fitting lid, and cook for 10 minutes. DO NOT LIFT THE LID UNDER ANY CIRCUMSTANCES. After 10 minutes, turn off the heat and let the chicken sit, covered, for an additional 10 minutes. Again, DO NOT LIFT THE LID. Once the time is up, you can finally remove the lid. (Your chicken will be cooked, but if you’re nervous check it with an instant-read thermometer and make sure it’s at least 165 degrees F.)
Place your chicken breasts on a cutting board and let them cool for a few minutes, and then dice them into roughly ½ inch cubes.
While the chicken is cooking, whisk together the remaining 2 tablespoon olive oil, both mustards, lemon juice, and honey until emulsified (aka smooth). Briefly set aside.
Heat a sauté pan over medium heat. (Don’t put any oil to the pan, peeps!) When hot, add the almonds and toast for 2-3 minutes, shaking the pan periodically, until golden brown and fragrant. Transfer to a bowl to cool.
Add the shallot, apple, pomegranate arils and tarragon to a mixing bowl with the diced chicken. Pour over the dressing and toss to coat. Taste and season with salt and fresh ground pepper. Add an extra squeeze of lemon if you feel like it.
Transfer the chicken salad to a serving bowl/plate and sprinkle with the toasted almonds. Serve with butter lettuce leaves if you like!