Step 1

Combine smoked paprika, paprika, salt, garlic powder, onion powder, pepper, oregano, thyme, and cayenne in wide, shallow bowl. Set wire rack in rimmed baking sheet. Wad up paper towel and place within reach of stove.

Step 2

Working with 1 chicken breast at a time, halve chicken breast crosswise, then cut thicker half in half horizontally, creating 3 cutlets of similar thickness. Place cutlets between sheets of plastic wrap and gently pound to even ⅓-inch thickness.

Step 3

Working with 1 cutlet at a time, dredge thoroughly in spice mixture, pressing to adhere, then shake off excess. Place cutlets in single layer on second rimmed baking sheet.

Step 4

Heat oil in 12-inch cast-iron skillet over high heat until just smoking. Add 1 tablespoon butter to skillet, then tilt skillet or spread butter with flexible spatula until it coats skillet evenly. Add 6 cutlets to skillet, press on each firmly with spatula, and cook undisturbed for 2 minutes. Using tongs, flip cutlets. Press cutlets against skillet with spatula and cook for 1 minute. Slide skillet off heat (leave burner on) and transfer cutlets to prepared wire rack. Grab paper towel with tongs and wipe out skillet to remove any debris.

Step 5

Return skillet to heat. Add remaining 2 tablespoons butter and repeat with remaining cutlets. Let cutlets rest for 3 minutes on rack and serve. (Leftover chicken can be refrigerated for up to 3 days.)