Combine all marinade ingredients except the olive oil in a large pan and bring to a boil; reduce the heat and simmer for 2 to 3 minutes. Remove from the heat and let cool to a room temperature.
Place the chicken breasts into a lidded container and pour the cooled marinade on top. Cover with the lid and refrigerate for 30 minutes to 2 hours.
Preheat the oven to 350°F and heat a heavy-duty grill pan on medium-high heat for about 5 minutes.
Pat-dry the marinated chicken breasts with paper towels and brush with the oil; place in the hot pan and grill for about 2 minutes per side to sear.
Add a couple of ice cubes to the pan and place in the oven. Roast the breasts for 15 to 18 minutes, or until cooked through and the internal temperature reaches 165°F.
Transfer the cooked chicken to a cutting board and tent loosely with aluminum foil; let rest for 5 to 10 minutes before slicing.
To make the bacon, heat a skillet over a medium-high heat with the diced bacon, cooking until crisp. Drain on a paper towel-lined plate.
Blend together all of the vinaigrette ingredients in a blender or with a whisk until emulsified and season to taste.
Toss the romaine and spring mix in a large bowl and divide between 4 salad bowls. Arrange the chicken slices, cherry tomatoes, eggs, blue cheese, onion, and bacon on top and serve with the dressing on the side.y