Prepare the brine by dissolving 1 tablespoon kosher salt in 2 cups cold water. Submerge chicken breasts fully and refrigerate for 30 minutes (no longer than 1 hour to prevent texture changes).
Remove chicken from brine, rinse briefly under cold water, and thoroughly pat dry with paper towels. Place between sheets of plastic wrap or parchment paper and pound to an even ½-inch thickness throughout.
Mix flour, garlic powder, paprika, and black pepper in a shallow dish. Pat chicken dry again, then lightly dust both sides with the flour mixture, shaking off excess.
Heat a heavy-bottomed skillet over medium-high heat until hot but not smoking. Add oil and heat until it shimmers but doesn't smoke (approximately 350°F).
Carefully place chicken breasts in the pan, allowing space between pieces. Cook undisturbed for 4-5 minutes until golden brown on the first side.
Reduce heat to medium-low. Flip chicken and add butter, thyme sprig, and crushed garlic (if using). Tilt the pan and spoon the melted butter over the chicken repeatedly for 4-5 minutes.
Cook until the internal temperature reaches 160°F at the thickest part (it will rise to 165°F during resting).
Transfer to a cutting board and rest, uncovered, for 5 minutes before slicing or serving.