Clarify butter: In a 3- to 4-qt. saucepan, gently simmer butter over medium heat. When foam stops rising to the surface, butter has turned clear, and milk solids coagulate on the bottom (about 1 hour), remove from heat and skim off foam with a spoon. Pour butter into a heavy 6- to 8-qt. dutch oven, leaving behind any solids in pot.
Meanwhile, cut potatoes lengthwise into batons about 1/3 in. thick and put in two very large bowls or a sink. Fill bowls with water and run your hands through potatoes to release starch. Drain and repeat until water runs clear. Spread potatoes on kitchen towels and blot dry. Insert a deep-fry thermometer into butter and bring to 250° over medium heat.
Line three or four rimmed baking sheets with parchment. In five or six large batches (it's okay to crowd the potatoes as long as they're covered with butter), blanch potatoes in butter until tender-crisp but not colored, about 2 minutes. Allow butter to return to 250° before cooking each new batch. Transfer fries to sheets as done (reserve butter for second frying) and chill until cold, at least 1 hour and up to 1 day.
Make herb sauce: In a medium saucepan, melt butter over medium heat. Mince capers and anchovies, then mash with flat side of chef's knife. Add with shallots to butter and remove from heat.
Bring 1 to 2 in. water to a boil in a medium saucepan. In a medium bowl, whisk egg yolks with mustard, vinegar, and lemon juice and set bowl over saucepan (not touching water). Cook, whisking constantly, until eggs start to thicken. Whisk in butter mixture, then herbs. Cook sauce, whisking, until butter begins to separate. Set aside.
About 1 hour before serving, preheat oven to 400° and bring reserved clarified butter to 375° over medium-high heat.
While butter heats, cook steaks: Heat a large cast-iron skillet over medium-high heat. Pat steaks dry and season generously on both sides with salt and freshly ground pepper.
When skillet is hot but not smoking, swirl in oil. Sear steaks until deeply browned and crusty underneath, about 3 minutes, pushing steaks around skillet while pressing down lightly on them so they brown evenly and well. Turn over and sear other sides the same way, about 2 minutes. Slide skillet into oven and cook steaks until medium-rare (125° to 130° on an instant-read thermometer), 5 to 6 minutes. Transfer steaks to a paper towel-lined board and let rest at least 10 minutes. Lower oven to 200°.
Finish potatoes: Gently loosen chilled potatoes from parchment (don't worry if they're stuck together). In several batches, fry potatoes in butter, stirring often with a slotted spoon, until medium golden and crisp, about 10 minutes per batch. Allow butter to return to temperature between batches, and transfer potatoes as done to rimmed baking sheets; season with salt and slide into oven to keep warm.
Reheat herb sauce over very low heat in a small pot until warm.
Melt 2 tbsp. butter in steak-frying skillet over medium-high heat. Add steaks and baste in foamy butter to reheat briefly.
Set each steak on a large dinner plate and spoon about 2 tbsp. herb sauce over it to cover completely. Heap fries next to steaks. Crack black pepper onto steaks, season with a little more salt, and serve.
*European-style Plugra butter has less water than American butters and is extra flavorful.
Make ahead: Clarified butter, up to 1 month, chilled. Herb sauce, up to 5 days, chilled. Frites, through step 4, up to 1 day; or fully cooked, up to 1 day (reheat in single layers at 450° until crisp, about 10 minutes).
Note: Nutritional analaysis is per serving with 2 tbsp. herb sauce.