Season the steak with salt and pepper and set aside. In a large mixing bowl, whisk together the lemon juice, shallot, mustard and anchovies. Let sit for 5 minutes, then whisk in the olive oil and heavy cream. Add the green beans and white beans; toss lightly.
Heat a large skillet over high. Swirl the canola oil over the bottom of the skillet. Add the steaks and sear until deeply browned and a crust has formed on the bottom, about 5 minutes. Turn the steak over and cook the other side an instant-read thermometer stuck into the thickest part reads 125ºF, about 3 minutes. Transfer to a cutting board, tent with foil and let rest for 10 to 15 minutes.
Add the arugula and ¼ cup of the Parmesan to the bowl with the beans mixture; toss to combine well. Transfer to a serving platter or divide among 4 plates. Slice the steak thinly against the grain and arrange on top of the salad. Drizzle with a little more olive oil and sprinkle with the remaining Parmesan.