Garlic-Butter Rib Roast

Place garlic cloves in a food processor, and process until almost a paste, about 2 minutes, stopping to scrape down sides as needed. Add shallot, rosemary, thyme, chives, anchovies, 1 tablespoon of the salt, and 2 teaspoons of the pepper to food processor. Pulse until shallot is finely chopped, about 5 pulses. Add butter, and process until combined, about 1 minute, stopping to scrape down sides as needed. Transfer half of butter mixture to a sheet of parchment paper; gently roll and shape into a log; refrigerate at least 1 hour or up to 3 days. Let remaining butter mixture stand at room temperature up to 4 hours, or transfer to a bowl, cover, and refrigerate for up to 3 days; let come to room temperature before continuing.

Season rib-eye roast evenly with remaining 1 tablespoon salt and 2 teaspoons black pepper. Using a spatula, spread butter mixture in bowl evenly over rib-eye roast, and transfer roast to a roasting pan fitted with a rack. Add 4 cups of the beef broth to roasting pan. Let stand at room temperature 1 hour.

Preheat oven to 450°F. Roast rib roast in preheated oven until lightly browned, 15 to 20 minutes. Without opening oven door, reduce oven temperature to 325°F, and continue roasting until a thermometer inserted into thickest portion of roast registers 130°F, about 1 hour and 40 minutes to 2 hours, occasionally checking liquid level in the bottom of roasting pan, and adding remaining 2 cups broth as needed to maintain a depth of at least 1/4 inch. Transfer rib-eye roast to a cutting board and let rest for 15 minutes.

Meanwhile, pour juices from roasting pan through a fine mesh strainer into a medium saucepan; discard solids. Bring to a simmer over low, skimming and discarding fat as it develops on the surface. Whisk together cornstarch and 3 tablespoons of simmering beef juices in a small bowl until smooth. Whisk cornstarch mixture into juices in saucepan, and continue simmering, whisking constantly, until sauce is thickened and coats back of a spoon, about 5 minutes. Remove saucepan from heat, and cover to keep warm.

Slice rib-eye roast against the grain into 1- to 1 1/2-inch-thick slices, and arrange on plates. Top each slice evenly with gravy mixture, 1/2-inch-thick rounds of chilled reserved compound butter, thinly sliced chives, flaky sea salt, and 2 or 3 grinds of pepper; serve immediately.