Dressing: Whisk together French’s Dijon Mustard, shallots, lemon juice, sugar, salt, and pepper. Gradually whisk in the olive oil until dressing is fully emulsified. Set aside.
Rub chicken breasts with olive oil. Sprinkle generously with salt and pepper.
Heat up an oiled skillet over medium-high heat. Cook chicken until seared on the first side, 3–4 minutes, then flip the chicken. Cover with a lid to allow the chicken to cook through, 7–10 minutes. Once the chicken is cooked through, remove from pan and let rest for 5–10 minutes, then cut into slices.
Cut the hard-boiled eggs into quarters. Cut the bacon into 1-inch (2 ½ cm) pieces.
Arrange the lettuce on a large platter. On top of the lettuce, place small piles of the chicken, eggs, bacon, tomatoes, radishes, cucumbers, and avocado.
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