An hour before cooking, season steaks with 2 tsp. salt and 1 tsp. pepper and set on a plate to come to room temperature. Then, brush steaks with 1 tbsp. oil. Meanwhile, soak 1 cup fruitwood chips in a bowl of water about 30 minutes.
Put 2 tbsp. butter in a shallow baking dish big enough to hold steaks. Add a few cracks of pepper and 1 tbsp. each thyme, honey, and vinegar; bring to grill area. Bring ingredients for peppers to grill: the Padróns; remaining 1 tbsp. oil, 1/4 tsp. salt, and 2 tbsp. butter; a dish with remaining 1 tbsp. thyme and the garlic; and another dish with remaining 1 tbsp. each honey and vinegar. Also bring a large cast-iron skillet, wooden spoon, grilling tongs, and foil.
For charcoal, ignite a very full chimney of hardwood mesquite charcoal on firegrate of a charcoal grill. Arrange coals on firegrate in a slope so there's a hotter area and a cooler one. Drain wood chips and scatter over charcoal. Set cooking grate in place. For gas, heat a gas grill to high (450° to 550°). Put drained wood chips in the grill's smoking box, or seal chips in a packet of foil, cut dime-size holes, and set directly on a burner. Cover grill.
When wood chips start to smoke (1 to 2 minutes for charcoal, 10 to 15 minutes for gas), set steaks over hottest part of charcoal fire (or anywhere on gas grill). Grill steaks covered, turning once and moving to cooler part of charcoal fire if they start to flare up, until well browned and done the way you like, about 10 minutes for medium-rare. Transfer steaks to baking dish with butter mixture, turn to coat, and tent loosely with foil.
Heat cast-iron skillet on cooking grate. When hot, add 1 tbsp. oil and swirl to coat. Then add peppers and 1/4 tsp. salt. Cook, shaking skillet and stirring occasionally, until peppers are browned and blistered, about 5 minutes. Add butter and let it foam and brown, 45 to 60 seconds. Stir in thyme, garlic, and honey-vinegar, then pour mixture over steaks. Let steaks rest about 1 minute more.
Transfer steaks to a cutting board, leaving juices and peppers in baking dish. Slice steaks crosswise into 1/2- to 3/4-in. strips. Using a spatula, pick up strips in original shape of steaks and set on a platter. Spoon about half of juices and peppers over steaks and serve the rest in a bowl on the side.