Using a meat mallet, pound chicken down to a uniform thickness of about 1/4-inch. Season each side with a bit of salt and coarsely ground pepper.
Heat a large skillet over medium-high heat. Add the 2 tbs of olive oil and when the oil shimmers, place chicken in the pan.
Brown well on both sides. Remove chicken and keep warm.
To make dressing, deglaze the pan with the 1/2 cup of chicken stock, making sure to scrape up all the browned bits. Turn heat to medium-high and reduce until there's about 2 tbs of liquid in the pan.
Remove from heat and stir in the lemon juice. Then whisk in the extra-virgin olive oil. Add any additional salt and pepper at this time. Also if you want a tangier dressing, feel free to add a few drops more of lemon juice. If you find the dressing too tart, stir in a pinch or two of sugar.
In a large bowl, mix the salad ingredients. Add about 2 tbs of the warm dressing and toss to coat.
Divide salad onto 2 plates and place chicken on top of salad. Drizzle remaining dressing over each plate.