Butterfly or Pound chicken to even thickness
Pat the chicken completely dry with paper towels.
Season both sides generously with salt and black pepper.
Place the all-purpose flour in a shallow dish. Dredge each piece of chicken in the flour, shaking off any excess.
Place a large stainless steel or cast-iron skillet over medium-high heat. Add the vegetable oil and swirl to coat.
Wait until the oil is shimmering and just starting to produce a faint wisp of smoke.
Carefully lay the chicken into the pan, laying it away from you to prevent oil splatters.
Do not move the chicken for at least 4 to 5 minutes. This is where patience is required.
Once the edges are visibly golden and the chicken lifts easily, flip it over.
Cook the second side for another 4 to 5 minutes.
Use a calibrated food thermometer to check the internal temperature. Once it reaches 165°F (74°C), immediately remove the chicken from the pan and place it on a warm plate.
Tent it loosely with aluminum foil.
Pour in the chicken broth and lemon juice. Use a wooden spoon or a whisk to aggressively scrape the bottom of the pan.
Add the dried thyme and let the liquid boil and reduce by about half, which should take 2 to 3 minutes.
Turn the heat down to low.
Take your cold unsalted butter and add it to the pan one tablespoon at a time. Whisk constantly.
Place the rested chicken back into the pan for 30 seconds just to coat it in the sauce and warm it through.
Transfer to serving plates, pour the remaining sauce over the top, and garnish with fresh parsley.