Preheat the oven to 400 degrees . In a small bowl, combine 1 tbsp. oil, the coffee, 2 tsp. salt and 1 tsp. pepper. Rub mixture all over the roast; let sit at room temperature for 30 minutes.
In a large heavy skillet (preferably cast-iron), heat 1 tsp. oil over medium-high heat. Sear the roast on all sides, about 6 minutes total. Transfer to a roasting pan and roast until a thermometer inserted into the thickest part registers 125 degrees for medium-rare, 15 to 20 minutes. Transfer the roast to a cutting board and let rest for 15 minutes.
Meanwhile, in a bowl, combine the parsley, garlic, zest and parmesan; season. Set aside gremolata. In a large skillet, heat the remaining 2 tsp. oil over medium-high heat. Add the green beans and 2 tbsp. water; season. Cook, covered, for 3 minutes. Toss; cook, uncovered, until crisp-tender, 2 minutes more. Remove from heat. Sprinkle with gremolata; toss to coat. Thinly slice the roast against the grain. Serve with green beans.