Preheat your oven to 425°F (220°C). Line a sheet pan with parchment for easy cleanup, or lightly oil it.
Pat the chicken thighs dry with a paper towel. This helps the skin get crispy. Season both sides with half a teaspoon of salt, pepper, paprika, and thyme.
In a large bowl, toss the halved potatoes with the olive oil, remaining salt, and a pinch of pepper until they’re evenly coated.
Spread the potatoes on the sheet pan in a single layer. Nestle the seasoned chicken thighs among the potatoes, skin side up.
Dot the pan with the remaining 1 tablespoon of butter, cut into small pieces. Add the minced garlic around the pan so it cooks in the butter and oils.
Roast in the oven for about 25–30 minutes, then spoon about 1/3 of the garlic butter over the chicken and potatoes. Return to the oven and roast for another 10–15 minutes, until the chicken reaches an internal temperature of 165°F (74°C) and the potatoes are tender and nicely browned.
If you like extra browning, broil on high for 1–2 minutes at the end, watching closely so nothing burns.
Remove from the oven. Let the dish rest for 5 minutes, then drizzle with the remaining garlic butter from the pan. Garnish with chopped parsley if you have it.