Place the chicken breasts one at a time in between to pieces of parchment paper or plastic wrap and pound to a ¼-inch thickness. You can use a meat mallet or a rolling pin. The idea is to get the chicken to an even thickness all around. Remove from the paper and place in a glass baking dish and squeeze the juice of 1 lemon on top. Drizzle with an equal amount of olive oil. Sprinkle with ½ teaspoon sea salt or kosher salt and black pepper to taste. Allow to sit at room temperature for 30-60 minutes.

Heat the grill to medium. In the meantime, prepare the salad dressing. Cut the garlic clove in half and rub the inside of a medium bowl with the cut side of the garlic. Add the garlic to the bowl. To the bowl, add 3 Tablespoons lemon juice, Dijon mustard, ½ teaspoon sea salt, and black pepper to taste. Whisk to combine. Pour ½ cup olive oil into the bowl, whisking constantly to emulsify. Taste for seasoning and tartness. Add more oil if necessary.

Remove chicken from marinade and grill a few minutes on both sides until golden brown. Place on a cutting board. Arrange the arugula on a platter and drizzle with enough of the dressing to coat lightly. Cut the chicken into strips and arrange on top of the arugula. Scatter tomatoes on top and drizzle a little more dressing. Or arrange the chicken on a platter and top with dressed arugula leaves and tomato.