1 1/2 to 2 pounds beef eye of round roast
1/2 cup EVOO, plus more for drizzling
Kosher salt and pepper
3 tablespoons chopped fresh rosemary
1 cup frozen green peas, thawed
About 1/4 cup fresh tarragon leaves
About 1/4 cup fresh mint leaves
1 cup fresh basil (about 20 leaves)
1 clove garlic, pasted
1/4 cup grated Parmigiano-Reggiano cheese
2 cups beef stock
2 (24-inch) loaves crusty French bread (at least 3 inches wide), cut into 6 (8-inch) lengths and split horizontally
Let the roast come to room temperature. Pat the meat dry, drizzle with EVOO, and season with a lot of salt and pepper. Sprinkle with the rosemary. Massage everything into the meat, all over.
Preheat the oven to 475°F.
Heat a Dutch oven or cast-iron skillet over medium-high heat. Add the meat and brown all over, about 5 minutes. Transfer the pan to the oven and roast to an internal temperature of 120°F, about 30 minutes. Transfer the roast to a cutting board and cover with foil. Let rest for 30 minutes.
Make-ahead: Cool, cover, and refrigerate.
Meanwhile, in a food processor, combine the peas, tarragon, mint, basil, garlic, Parm, 1/2 cup EVOO, and salt and pepper, and process to almost smooth.
Make-ahead: Transfer to small container and refrigerate.
Night of: Return the meat and pesto to room temp.
To serve, very thinly slice the meat. Heat the beef stock to warm but not boiling. Quickly dip the sliced meat in the broth and place on the bottom of a length of French bread, top with green pea pesto, and set the bread top in place.