Season steak with 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1/4 teaspoon garlic powder. Let steak come to room temperature for at least 15 minutes.
Heat 1 tablespoon oil in a 12-inch cast iron skillet over medium-high heat until smoking. Be sure to turn on your oven vent—things are going to get smoky! Add steak and arrange garlic and thyme next to the steak. Sear steak until a dark golden-brown crust forms on the bottom, about 3 minutes.
Flip steak and add 2 tablespoons butter to the skillet. Baste steak with melted butter by tilting the pan and spooning the pooled butter over the steak. Continue cooking steak until the other side is also golden-brown, 2 to 3 minutes, and an internal thermometer registers 130 degrees F for medium-rare. Transfer steak to a plate, return skillet to stovetop, and reduce heat to medium. Let steak rest for at least 10 minutes.
Add potatoes to the skillet, cut-side down in the hot leftover oil and butter, and cook until golden-brown, 2 to 3 minutes.
Pour all accumulated juices from under the steak over the potatoes. Turn potatoes, season with salt, and continue cooking until browned, about 2 minutes more. Transfer potatoes to a plate and scrape pan juices over them.
Return skillet to medium heat. Melt remaining tablespoon butter in the skillet. Stir Swiss chard into melted butter and season with 1/2 teaspoon garlic powder, salt, and pepper. Stir in lemon juice or vinegar and sauté until wilted, 2 to 3 minutes.
Cut rested steak into 1/2-inch-thick slices. Divide steak, potatoes, and Swiss chard between two plates to serve.