Pat the chicken dry with paper towels. Season both sides with 3/4 tsp kosher salt, 1/4 tsp black pepper, and the smoked paprika. If breasts are uneven, place them between plastic wrap and gently pound to an even 3/4" thickness so they cook evenly.

Heat a 10-12 inch skillet over medium-high until hot. Add 1 tbsp olive oil and swirl. Place the chicken in the pan (do not crowd) and sear without moving until golden brown, about 4-5 minutes. Flip and sear the second side 3-4 minutes until nicely browned.

Reduce heat to medium-low, add 1 tbsp of the butter to the pan, tilt and spoon melted butter over the chicken for 1 minute. Check internal temperature with an instant-read thermometer — remove chicken from the pan at 160°F; it will finish to 165°F while resting. Transfer chicken to a plate and tent loosely with foil to rest 5-7 minutes.

With the skillet over medium heat, add the remaining 3 tbsp butter. When melted, add the minced garlic and cook, stirring, until fragrant and just beginning to color, about 30-45 seconds. Pour in 1/4 cup chicken stock (or wine) to deglaze, scraping up browned bits, and simmer 1-2 minutes until slightly reduced. Stir in the lemon juice and chopped thyme, then taste and add remaining 1/4 tsp kosher salt and remaining black pepper if needed.

Return the chicken to the skillet briefly, spooning sauce over each piece to warm for 30 seconds. Transfer to plates, spoon extra garlic-lemon butter over the chicken, garnish with chopped parsley and lemon wedges, and serve immediately.