Prepare a large bowl of ice water (about half ice), and bring a large pot of salted water to a boil. Place the green garlic in a fine mesh strainer, and submerge the strainer in the pot of boiling water for just 7 seconds. Transfer the strainer (with the green garlic in it) to the ice water bath until completely chilled. Drain excess water and spread the green garlic on a clean kitchen towel and pat it dry. 

Place the green garlic in a blender and blend on high for 3-5 minutes, until smooth, adding up to a tablespoon of water if needed to keep the blades moving. Transfer to a large mixing bowl. Add the butter, parsley, shallots, lemon zest, lemon juice, Worcestershire sauce, the kosher salt, black pepper, and anchovy paste. Use a rubber spatula to incorporate all the ingredients, blending well until thoroughly combined (this will take a couple minutes - you can also use a stand mixer fitted with a paddle attachment). 

Divide the butter into two portions, and place each one on a sheet of parchment or wax paper. Roll the bottom half of the paper over the butter, and with one hand hold the bottom layer in place and with the other hand pull the covered butter toward you. Wrap your fingers tightly around the butter to roll it up. Twist the ends of paper to seal, and chill in the fridge until hard, about 2 hours. Remove one of the rolls from the fridge about 25 minutes before serving (see note).

Preheat oven to 250℉. Set a rack in a roasting pan.

Sprinkle the rib eye with a generous amount of salt and pepper. Heat a cast-iron skillet over high heat. Pour in about 1/4 inch of canola oil. When hot, place the beef fat-side-down in the oil. Sear until golden brown, 3-5 minutes. Sear the same way on all sides, then remove from heat.

Arrange the thyme and rosemary sprigs across the rack in the roasting pan. Set the two garlic halves on top. Place the rib eye on top of the garlic and herbs with the fat side facing up. Roast for 2 hours 45 minutes, until an instant read thermometer inserted into it reads 125℉. Let rest in the roasting pan for about 25 minutes before transferring to a cutting board to carve. While the beef is resting, baste several times with pan juices. 

Carve the rib eye into 6 slices, and serve each slice with a 1/2-inch disk of green garlic-parsley butter.