Using paper towels, pat both sides of the chicken dry; season with salt and pepper, to taste.
Heat canola oil in a large cast iron skillet over medium heat. Working in batches, add chicken to the skillet in a single layer and cook until golden brown, about 4-5 minutes.
Reduce heat to medium low. Using tongs, flip and cook, covered, until cooked through, reaching an internal temperature of 165 degrees F, an additional 8 minutes. Set aside and keep warm.
Melt 1 tablespoon butter in the skillet over medium low heat. Add garlic, shallot and rosemary, and cook, stirring frequently, until fragrant, about 2 minutes; season with salt and pepper, to taste.
Whisk in flour until lightly browned, about 1 minute.
Stir in chicken stock, scraping any browned bits from the bottom of the skillet. Bring to a boil; reduce heat and simmer, stirring occasionally, until reduced and thickened, about 4-5 minutes.
Stir in lemon juice and remaining 1 tablespoon butter; season with salt and pepper, to taste. Return chicken to the skillet.
Serve immediately.
Notes
Pat the chicken dry. Before seasoning the chicken, pat the chicken breasts completely dry with paper towels to remove any surface moisture.
Use a cast iron skillet. Cast iron skillets retain heat much better than a nonstick skillet, allowing for even cooking and a better sear on the chicken.
Cook in batches. An overcrowded pan can lead to uneven cooking and poor browning. Work in batches to maintain high heat for a good sear and a golden brown crust on each chicken breast, yielding juicier, tender meat.
Cover the skillet. This will trap steam and heat, allowing the chicken breasts to cook through completely without drying out the exterior.
Use an instant-read thermometer for the most accurate results. The internal temperature should reach 165°F.
Let your meat rest. Let your chicken rest for at least 5 minutes prior to serving, allowing the juices to redistribute – this will allow for maximum flavor and juiciness.
Deglaze the pan. Deglaze the skillet with chicken stock, lifting up all the browned bits from the bottom of the skillet to capture maximum flavor and to build a rich pan sauce for the chicken.
Use freshly squeezed lemon juice. While bottled lemon juice can work in a pinch, freshly squeezed is ideal here for its vibrant, stronger flavors.
Reheat in the oven. Leftover chicken can be rubbery when reheated. For best results with leftovers, reheat in the oven at 350°F, covered in aluminum foil, until warmed through.