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Step 1
If your chicken is thicker than 1/2-inch after slicing it in half, pound it to 1/2-inch thickness. Or, leave it thicker and add a few minutes to the cooking time.
Step 2
Set up a workstation: on the left, put all of your chicken on a cutting board; season with salt and pepper on both sides. In the middle, place the flour in a wide, shallow dish. On the right, have another plate ready for your floured chicken. Gently toss each chicken breast in the flour, shaking off the excess, and set aside.
Step 3
Heat 3 tablespoons oil in a 12-inch skillet over medium heat. Make sure the oil is hot enough by splashing a bit of water in there; it should crackle and sizzle immediately. When oil is hot, add half the chicken. Cook 4-5 minutes on the first side until it's golden brown and crisp, then flip and cook another 2-3 minutes on the second side. Transfer to a plate. Add another 3 tablespoons of oil and repeat with remaining chicken.
Step 4
Heat another tablespoon of oil in the same skillet over low heat (you might need to turn the skillet off to let it cool down, you don't want the garlic to burn). Add garlic, artichoke hearts and capers and cook until garlic is softened and fragrant, about 2 minutes. Increase heat to medium and add lemon juice and 1/2 cup of water. Simmer 4-6 minutes or until liquid has reduced slightly, it should look thickened. Reduce heat to low and stir in parsley and butter until it has melted and emulsified into a sauce.
Step 5
Turn off heat, taste and season the sauce as desired. If it's too lemony for your tastes, add another splash of water and adjust seasoning as needed.
Step 6
Add chicken back to pan and flip to coat it in the sauce. Re-heat the chicken with sauce for 1 minute. Transfer to plates to serve, or eat straight from the skillet, with a piece of bread or cooked pasta for dunking.