In a shallow dish, combine the flour, salt and pepper and whisk to combine and set aside.
SAUTE THE MUSHROOMS AND SHALLOTS
Place a large skillet over medium high heat for 45 seconds to a minute. Add 2 teaspoons of olive oil. The oil will slick across the pan and shimmer.
Tilt the pan to coat with olive oil, then add the sliced mushrooms. Spread the mushrooms into a single even layer, and saute until lightly browned, stirring occasionally. Transfer the mushrooms to a small dish.
Add 1 teaspoon olive oil to the pan and stir in the shallots. Cook for 1-2 minutes until they are softened and fragrant. Transfer the shallots to the dish with the mushrooms.
COOK THE CHICKEN BREASTS:
Pat the chicken breasts dry with paper towels and press the chicken breasts one at a time into the dredge. Lightly coat the breasts on all sides with the flour mixture and shake off the excess.
Heat the remaining tablespoon of olive oil in the skillet over medium high heat. Carefully place the flour coated chicken to the pan and cook for 3-4 minutes on one side without turning or touching the chicken, until browned and golden.
Use tongs to flip the chicken and continue to cook for 3-4 more minutes to brown.
DEGLAZE THE PAN:
Add the white wine to the pan and stir, scraping up the browned bits from the bottom of the pan. Cook for 2-3 minutes or until the wine is reduced by about half.
ASSEMBLE LEMON ARTICHOKE CHICKEN
Add the chicken broth, sauteed mushrooms and shallots, artichokes, bundle of thyme, sliced lemons and capers. Stir to combine and spread everything out evenly in the pan. Turn the heat to medium low and place the lid slightly askew on the pan so that steam can escape.
Simmer for 10 minutes or until the chicken breasts are cooked through. Use the tongs to fish out the thyme sprigs and sliced lemons. Discard. Add the knob of butter and stir to form a silky sauce. Taste for seasonings and adjust with additional salt or pepper as needed.