Preheat the oven to 275°F. Heat a castiron skillet over medium-high heat.
Season both sides of steak generously with salt and pepper. Let rest and come to room temp, about 15 minutes. Place the steak on a wire rack over a baking sheet. Top with a couple of sprigs of thyme and 1tbsp of butter each. Put into the oven on the center rack. Cook for 20 minutes.
Meanwhile, add diced chili peppers, red onion, grape tomatoes, and red pepper flakes to a food processor. Pulse 3 to 4 times to break up the vegetables.
Wash and dice the potatoes. Add 1 tablespoon olive oil to the cast iron skillet and carefully add the potatoes. Sprinkle a pinch of salt and pepper over the potatoes and cook for 2 minutes. Add the chili relish. Saute for 5 minutes. Remove from heat and set aside.
Remove the steak from the oven and let rest for 10 minutes. While resting, rinse cast iron and place back over high heat.
Place steak into the cast iron to sear. Add 2 tbsp butter, thyme sprigs, and whole garlic cloves. Cook for 1 minute, then using tongs render the fat on the side of the steak for about 30 seconds. Flip to the other side and cook for 1 minute. Add remaining butter and lower heat to medium. Tilt the pan and spoon butter over the steak continuously for 2 minutes. Flip steak again, and baste with butter for 2 more minutes. Remove the steaks from heat and let rest. Keep the cast iron on the stovetop and do not drain, you will fry the eggs in the next step in them. Check the temperature of the steak using a meat thermometer. Keep in mind the steak will continue to rise in temp as it rests another 5-7°. For medium-rare, the temperature should be 125° at the time of removal. For medium, 130°.
While the steak rests, cook the eggs. Carefully crack eggs into the cast iron skillet and fry in the leftover butter/ fat for a delicious flavor. Fry for 1 to 2 minutes. Do not flip the eggs. If you prefer a more well-done yolk, cook an additional 1 to 2 minutes.
Plate the potatoes on one side of your dish, add the new york strip to the other and top the potatoes with fried eggs. Garnish with fresh cracked peppercorn and micro greens (optional) and Enjoy!