Make the garlic herb butter: in a food processor, pulse the parsley, chives, garlic, olive oil, 3/4 teaspoon kosher salt, and 1/4 teaspoon black pepper until the herbs are finely chopped and combined.
Add the softened unsalted butter and lemon juice to the food processor and blend until fully incorporated.
Scrape the compound butter onto parchment paper, roll into a tight log, twist the ends to seal, and chill in the refrigerator for about 2 hours to firm.
Preheat the oven to 250°F (120°C). Season the rib-eye steak generously on all sides with kosher salt and freshly ground black pepper.
Place the steak on a baking sheet fitted with a rack and roast in the oven until an instant-read thermometer inserted into the thickest part reads 125°F for medium-rare, about 45–55 minutes.
Remove the steak from the oven and let it rest for 5 minutes while you heat a cast-iron skillet over medium-high heat until smoking hot.
Sear the steak in the hot skillet, pressing slightly, until a deep golden crust forms, about 45 seconds per side.
Transfer the steak to a cutting board and let it rest for 10 minutes, then slice and serve with slices of the chilled garlic herb butter.